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    Wyświetlanie 1-40 z 40
    Tytuł:
    Axisymmetric solutions to the Cauchy problem for time-fractional diffusion equation in a circle
    Autorzy:
    Povstenko, Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/121736.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
    Tematy:
    Cauchy problem
    circle
    Caputo fractional derivative
    problem Cauchy'ego
    koło
    Opis:
    The Cauchy problems for time-fractional diffusion equation with delta pulse initial value of a sought-for function is studied in a circle domain in the axisymmetric case under zero Dirichlet and Neumann boundary conditions, respectively. The Caputo fractional derivative is used. The Laplace and finite Hankel integral transforms are employed. The results are illustrated graphically.
    Źródło:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2010, 15; 109-117
    2450-9302
    Pojawia się w:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of the fundamental solution of a second order evolution equation
    Autorzy:
    Bochenek, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/1294733.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    evolution problem
    stable family of operators
    stable approximations of the evolution operator
    fundamental solution
    Cauchy problem
    uniformly correct Cauchy problem
    Opis:
    We give sufficient conditions for the existence of the fundamental solution of a second order evolution equation. The proof is based on stable approximations of an operator A(t) by a sequence ${A_n(t)}$ of bounded operators.
    Źródło:
    Annales Polonici Mathematici; 1997, 66, 1; 15-35
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Monotonic solutions of multi term fractional differential equations
    Autorzy:
    Salem, Hussein A. H.
    Powiązania:
    https://bibliotekanauki.pl/articles/745873.pdf
    Data publikacji:
    2007
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Fractional calculus
    fixed point theorem
    Cauchy problem
    Opis:
    In this paper, we present an existence of monotonic solutions for a nonlinear multi term non-autonomous fractional differential equation in the Banach space of summable functions. The concept of measure of noncompactness and a fixed point theorem due to \(G\). Emmanuele is the main tool in carring out our proof.
    Źródło:
    Commentationes Mathematicae; 2007, 47, 1
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Cauchy problem and self-similar solutions for a nonlinear parabolic equation
    Autorzy:
    Biler, Piotr
    Powiązania:
    https://bibliotekanauki.pl/articles/1289308.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    nonlinear parabolic-elliptic system
    Cauchy problem
    self-similar solutions
    Opis:
    The existence of solutions to the Cauchy problem for a nonlinear parabolic equation describing the gravitational interaction of particles is studied under minimal regularity assumptions on the initial conditions. Self-similar solutions are constructed for some homogeneous initial data.
    Źródło:
    Studia Mathematica; 1995, 114, 2; 181-205
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On α-times integrated C-semigroups and the abstract Cauchy problem
    Autorzy:
    Kuo, Chung-Cheng
    Shaw, Sen-Yen
    Powiązania:
    https://bibliotekanauki.pl/articles/1205940.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    generator
    abstract Cauchy problem
    α-times integrated C-semigroup
    Opis:
    This paper is concerned with α-times integrated C-semigroups for α > 0 and the associated abstract Cauchy problem: $u'(t) = Au(t) + \frac{t^{α-1}}{Γ(α)}x$, t >0; u(0) = 0. We first investigate basic properties of an α-times integrated C-semigroup which may not be exponentially bounded. We then characterize the generator A of an exponentially bounded α-times integrated C-semigroup, either in terms of its Laplace transforms or in terms of existence of a unique solution of the above abstract Cauchy problem for every x in $(λ-A)^{-1}C(X)$.
    Źródło:
    Studia Mathematica; 2000, 142, 3; 201-217
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On k-summability of formal solutions for certain partial differential operators with polynomial coefficients
    Autorzy:
    Ichinobe, K.
    Miyake, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255468.pdf
    Data publikacji:
    2015
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    k-summability
    Cauchy problem
    power series solutions
    successive approximation
    Opis:
    We study the k-summability of divergent formal solutions for the Cauchy problem of certain linear partial differential operators with coefficients which are polynomial in t. We employ the method of successive approximation in order to construct the formal solutions and to obtain the properties of analytic continuation of the solutions of convolution equations and their exponential growth estimates.
    Źródło:
    Opuscula Mathematica; 2015, 35, 5; 625-653
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations. Part. 1
    Autorzy:
    Pytel-Kudela, M.
    Prykarpatsky, A.K.
    Powiązania:
    https://bibliotekanauki.pl/articles/254883.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    dissolving operators
    bilinear forms
    Cauchy problem
    semigroups
    evolution equations
    Opis:
    The analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations in Hilbert spaces are studied using theory of bilinear forms in respectively rigged Hilbert spaces triples. Theorems specifying the existence of a dissolving operator for a class of adiabatically perturbed nonautonomous partial differential equations are stated. Some applications of the results obtained are discussed.
    Źródło:
    Opuscula Mathematica; 2006, 26, 1; 131-136
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Weakly nonlinear boundaty value problems for differential systems with impulse action
    Slabonelinejjnye kraevye zadachi dlja sistem differencial'nykh uravnenijj s impul'snym vozdejjstviem
    Autorzy:
    Ovchar, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/76835.pdf
    Data publikacji:
    2013
    Wydawca:
    Komisja Motoryzacji i Energetyki Rolnictwa
    Tematy:
    nonlinear boundary value problem
    linear boundary value problem
    differential equation
    Cauchy problem
    Opis:
    Coefficient obtained sufficient conditions for the existence and iterative algorithm of solutions of weakly nonlinear boundary value problems for ordinary differential equations with impulse action in general, when the number of boundary conditions does not coincide with the order of the differential system.
    Коэффициенты получены с достаточных условий для существования и итерационного алгоритма решения через слабо нелинейни краеви задачи для обыкновенных дифференциальных уравнений с импульсным воздействием в общем случае, когда число граничных условий не совпадает с порядком дифференциального системы.
    Źródło:
    Motrol. Motoryzacja i Energetyka Rolnictwa; 2013, 15, 3
    1730-8658
    Pojawia się w:
    Motrol. Motoryzacja i Energetyka Rolnictwa
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Abstract parabolic problem with non-Lipschitz nonlinearity
    Autorzy:
    Cholewa, Jan
    Dlotko, Tomasz
    Powiązania:
    https://bibliotekanauki.pl/articles/1207637.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    dissipative semigroup
    parabolic system
    Cauchy problem
    global attractor
    global solution
    Opis:
    An abstract parabolic equation with sectorial operator and continuous nonlinearity is studied in this paper. In particular, the asymptotic behavior of solutions is described within the framework of the theory of global attractors. Examples included in the final part of the paper illustrate the presented ideas.
    Źródło:
    Banach Center Publications; 2000, 52, 1; 73-81
    0137-6934
    Pojawia się w:
    Banach Center Publications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hyperbolic Cauchy problem and Lerays residue formula
    Autorzy:
    Tanabé, Susumu
    Powiązania:
    https://bibliotekanauki.pl/articles/1207980.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Leray's residue formula
    Gauss-Manin connexion
    Bonn
    hyperbolic Cauchy problem
    Opis:
    We give an algebraic description of (wave) fronts that appear in strictly hyperbolic Cauchy problems. A concrete form of a defining function of the wave front issued from the initial algebraic variety is obtained with the aid of Gauss-Manin systems satisfied by Leray's residues.
    Źródło:
    Annales Polonici Mathematici; 2000, 74, 1; 275-290
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fundamental solution to the Cauchy problem for the time-fractional advection-diffusion equation
    Autorzy:
    Povstenko, Y.
    Klekot, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/122910.pdf
    Data publikacji:
    2014
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Cauchy problem
    Mittag-Leffler function
    time-fractional diffusion-wave equation
    Opis:
    The one-dimensional time-fractional advection-diffusion equation with the Caputo time derivative is considered. The fundamental solution to the Cauchy problem is obtained using the integral transform technique. The numerical results are illustrated graphically.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 1; 95-102
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the method of calculation of buckling and post-buckling behavior of laminated shells with small arbitrary imperfections
    O metodzie obliczania wyboczenia i stanu powyboczeniowego dla powłok z małymi imperfekcjami
    Autorzy:
    Semenyuk, M.
    Trach, V.
    Zhukova, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/2084048.pdf
    Data publikacji:
    2021
    Wydawca:
    Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Wydawnictwo Szkoły Głównej Gospodarstwa Wiejskiego w Warszawie
    Tematy:
    buckling
    post-buckling
    imperfection
    laminated shell
    mode interaction
    Cauchy problem
    Opis:
    In the present paper the variant of computational methods of stability and initial post-buckling behavior of isotropic shells was generalized with respect to laminated composite shells. Using methods of the asymptotic analysis of the Timoshenko–Mindlin theory, the relationships for calculation of shells with the small geometrical imperfections of the different shapes have been produced. On the basis of obtained equations, the technique of calculation of a non-linear pre-buckling state, limiting loads and bifurcation, and also initial post-buckling behavior of laminated cylindrical shells at an axial compression and external pressure have been worked out. The results of calculation for the shells made of glass fiber-reinforced plastic and carbon fiber-reinforced plastic with multimodal imperfections and dimple imperfections have been presented. The features of transformation of the interacting modes of imperfections have been researched.
    Źródło:
    Acta Scientiarum Polonorum. Architectura; 2021, 20, 2; 17-25
    1644-0633
    Pojawia się w:
    Acta Scientiarum Polonorum. Architectura
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An existence theorem for set differential inclusions in a semilinear metric space
    Autorzy:
    De Blasi, F. S.
    Lakshmikantham, V.
    Bhaskar, T. G.
    Powiązania:
    https://bibliotekanauki.pl/articles/970280.pdf
    Data publikacji:
    2007
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    approximate continuous selections
    Cauchy problem
    set differential inclusions
    Hukuhara derivative
    Opis:
    Using the notion of continuous approximate selections, we establish an existence theorem for set differential inclusions in a semi-linear metric space.
    Źródło:
    Control and Cybernetics; 2007, 36, 3; 571-582
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of fundamental solutions to fractional diffusion-wave equation in polar coordinates
    Autorzy:
    Povstenko, Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/121886.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
    Tematy:
    równanie ułamkowe
    problem Cauchy'ego
    transformaty Laplace'a
    transformata Hankela
    fractional equations
    Cauchy problem
    Laplace transforms
    Hankel and Laplace transforms
    Opis:
    The diffusion-wave equation is a mathematical model of a wide range of important physical phenomena. The first and second Cauchy problems and the source problem for the diffusion-wave equation are considered in cylindrical coordinates. The Caputo fractional derivative is used. The Laplace and Hankel transforms are employed. The results are illustrated graphically.
    Źródło:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2009, 14; 97-104
    2450-9302
    Pojawia się w:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Monotone iteration for infinite systems of parabolic equations
    Autorzy:
    Pudełko, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/255193.pdf
    Data publikacji:
    2005
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    infinite systems
    parabolic equations
    Cauchy problem
    monotone iteration method
    differentail inequality
    Opis:
    In the paper the Cauchy problem for and infinite system of parabolic type equations is studied. The general operators of the parabolic type of second order with variable coefficients are considered and the system is weakly coupled. Among the obtained results there is a theorem on differential inequality as well as the existence and uniqueness theorem in the class of continuous-bounded functions obtained by monotone iterative method.
    Źródło:
    Opuscula Mathematica; 2005, 25, 2; 307-318
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solution of inverse heat conduction equation with the use of Chebyshev polynomials
    Autorzy:
    Joachimiak, M.
    Frąckowiak, A.
    Ciałkowski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/239926.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    Laplace’s equation
    boundary inverse problem
    quasi-Cauchy problem
    stability of the inverse problem
    równanie Laplace'a
    brzegowe zagadnienie odwrotne
    Problem Quasi-Cauchy'ego
    Opis:
    A direct problem and an inverse problem for the Laplace’s equation was solved in this paper. Solution to the direct problem in a rectangle was sought in a form of finite linear combinations of Chebyshev polynomials. Calculations were made for a grid consisting of Chebyshev nodes, what allows us to use orthogonal properties of Chebyshev polynomials. Temperature distributions on the boundary for the inverse problem were determined using minimization of the functional being the measure of the difference between the measured and calculated values of temperature (boundary inverse problem). For the quasi-Cauchy problem, the distance between set values of temperature and heat flux on the boundary was minimized using the least square method. Influence of the value of random disturbance to the temperature measurement, of measurement points (distance from the boundary, where the temperature is not known) arrangement as well as of the thermocouple installation error on the stability of the inverse problem was analyzed.
    Źródło:
    Archives of Thermodynamics; 2016, 37, 4; 73-88
    1231-0956
    2083-6023
    Pojawia się w:
    Archives of Thermodynamics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Explicit Finite-Difference Scheme for the Numerical Solution of the Model Equation of Nonlinear Hereditary Oscillator with Variable-Order Fractional Derivatives
    Autorzy:
    Parovik, R. I.
    Powiązania:
    https://bibliotekanauki.pl/articles/229615.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    nonlinear hereditary oscillator
    finite difference scheme
    Cauchy problem
    fractional derivatives
    numerical experiment
    Opis:
    The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution
    Źródło:
    Archives of Control Sciences; 2016, 26, 3; 429-435
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Retarded functional differential equations in Banach spaces and Henstock-Kurzweil-Pettis integrals
    Autorzy:
    Sikorska-Nowak, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/729411.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    pseudo-solution
    Pettis integral
    Henstock-Kurzweil integral
    Henstock-Kurzweil-Pettis integral
    Cauchy problem
    Opis:
    We prove an existence theorem for the equation x' = f(t,xₜ), x(Θ) = φ(Θ), where xₜ(Θ) = x(t+Θ), for -r ≤ Θ < 0, t ∈ Iₐ, Iₐ = [0,a], a ∈ R₊ in a Banach space, using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of the measure of weak noncompactness.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 315-327
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On some qualitative properties of integrable solutions for Cauchy-type problem of fractional order
    Autorzy:
    Metwali, M. M. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/357698.pdf
    Data publikacji:
    2017
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    Cauchy problem
    Darbo fixed point theorem
    quadratic integral equations
    measure of noncompactness
    problem Cauchy'ego
    twierdzenie o punkcie stałym
    twierdzenie Darbo
    równania całkowe
    miara niezwartości
    Opis:
    The paper discusses the existence of solutions for Cauchy-type problem of fractional order in the space of Lebesgue integrable functions on bounded interval. Some qualitative properties of solutions are presented such as monotonicity, uniqueness and continuous dependence on the initial data. The main tools used are measure of weak (strong) noncompactness, Darbo fixed point theorem and fractional calculus.
    Źródło:
    Journal of Mathematics and Applications; 2017, 40; 121-p134
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    $L^p$-$L^q$-Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity
    Autorzy:
    Gawinecki, Jerzy
    Powiązania:
    https://bibliotekanauki.pl/articles/1313322.pdf
    Data publikacji:
    1991
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    decay estimates
    partial differential equations
    Cauchy problem
    symmetric hyperbolic system of first order
    linear thermoelasticity
    Opis:
    We prove the $L^p$-$L^q$-time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman's approach [12], [5] to the $L^p$-$L^q$-time decay estimates.
    Źródło:
    Annales Polonici Mathematici; 1991, 54, 2; 135-145
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Selfsimilar profiles in large time asymptotics of solutions to damped wave equations
    Autorzy:
    Karch, Grzegorz
    Powiązania:
    https://bibliotekanauki.pl/articles/1205809.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    generalized wave equation with damping
    the Cauchy problem
    large time behavior of solutions
    selfsimilar solutions
    Opis:
    Large time behavior of solutions to the generalized damped wave equation $u_{tt} +A u_t +ν B u+F(x,t,u,u_t,∇ u) = 0$ for $(x,t)∈ ℝ^n × [0,∞)$ is studied. First, we consider the linear nonhomogeneous equation, i.e. with F = F(x,t) independent of u. We impose conditions on the operators A and B, on F, as well as on the initial data which lead to the selfsimilar large time asymptotics of solutions. Next, this abstract result is applied to the equation where $Au_t = u_t$, $Bu = -Δu$, and the nonlinear term is either $|u_t|^{q-1}u_t$ or $|u|^{α-1}u$. In this case, the asymptotic profile of solutions is given by a multiple of the Gauss-Weierstrass kernel. Our method of proof does not require the smallness assumption on the initial conditions.
    Źródło:
    Studia Mathematica; 2000, 143, 2; 175-197
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Tauberian theorems for vector-valued Fourier and Laplace transforms
    Autorzy:
    Chill, Ralph
    Powiązania:
    https://bibliotekanauki.pl/articles/1218589.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Tauberian theorem
    Fourier transform
    Laplace transform
    asymptotically almost periodic
    analytic Radon-Nikodym property
    Cauchy problem
    Opis:
    Let X be a Banach space and $f ∈ L^1_loc(ℝ;X)$ be absolutely regular (i.e. integrable when divided by some polynomial). If the distributional Fourier transform of f is locally integrable then f converges to 0 at infinity in some sense to be made precise. From this result we deduce some Tauberian theorems for Fourier and Laplace transforms, which can be improved if the underlying Banach space has the analytic Radon-Nikodym property.
    Źródło:
    Studia Mathematica; 1998, 128, 1; 55-69
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Differential inclusions and multivalued integrals
    Autorzy:
    Cichoń, Kinga
    Cichoń, Mieczysław
    Satco, Bianca
    Powiązania:
    https://bibliotekanauki.pl/articles/729320.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    nonlocal Cauchy problem
    Aumann integrals
    Pettis integrals
    Henstock-Kurzweil-Pettis integrals
    measure of weak noncompactness
    Opis:
    In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces
    x'(t) ∈ F(t,x(t)), x(0)=g(x), t ∈ [0,T] = I.
    Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We concentrate on the problems for which the assumptions are expressed in terms of the weak topology in a Banach space. We recall and improve earlier papers of this type. The paper is complemented by a short survey about multivalued integration including Pettis and Henstock-Kurzweil-Pettis multivalued integrals.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 2; 171-191
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An existence result for impulsive functional differential inclusions in Banach spaces
    Autorzy:
    Benedetti, Irene
    Powiązania:
    https://bibliotekanauki.pl/articles/729505.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    impulsive functional differential inclusion
    semilinear differential inclusion
    mild solution
    Cauchy problem
    solution set
    condensing multimap
    fixed point
    Opis:
    We use the topological degree theory for condensing multimaps to present an existence result for impulsive semilinear functional differential inclusions in Banach spaces. Moreover, under some additional assumptions we prove the compactness of the solution set.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2004, 24, 1; 13-30
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On a multivalued second order differential problem with Hukuhara derivative
    Autorzy:
    Piszczek, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255779.pdf
    Data publikacji:
    2008
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Hukuhara's derivative
    multivalued cosine families
    Riemann integral for multifunctions
    Cauchy problem for a set-valued differential equation
    Opis:
    Let K be a closed convex cone with the nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. Assume that continuous linear multifunctions H, ψ : K → cc(K) are given. We consider the following problem D2 φ (t, x) = φ (t, H(x)), D φ (t,x) / (t=0) = {0}, φ (0, x) = ψ (x) for t ≥ 0 and x ∈ K, where D φ (t, x) denotes the Hukuhara derivative of φ (t, x) with respect to t.
    Źródło:
    Opuscula Mathematica; 2008, 28, 2; 151-161
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Multivalued linear operators and differential inclusions in Banach spaces
    Autorzy:
    Baskakov, Anatolii
    Obukhovskii, Valeri
    Zecca, Pietro
    Powiązania:
    https://bibliotekanauki.pl/articles/729521.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    multivalued linear operator
    generalized semigroup
    minimal growth at infinity
    Hille-Yosida condition
    degenerate differential inclusion
    Cauchy problem
    bounded solution
    Opis:
    In this paper, we study multivalued linear operators (MLO's) and their resolvents in non reflexive Banach spaces, introducing a new condition of a minimal growth at infinity, more general than the Hille-Yosida condition. Then we describe the generalized semigroups induced by MLO's. We present a criterion for an MLO to be a generator of a generalized semigroup in an arbitrary Banach space. Finally, we obtain some existence results for differential inclusions with MLO's and various types of multivalued nonlinearities. As a consequence, we give theorems on the existence of local, global and bounded solutions of the Cauchy problem for degenerate differential inclusions.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2003, 23, 1; 53-74
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Nonlinear Differential Equations in Generalized Musielak-Orlicz Spaces
    Autorzy:
    Kozlowski, W.M.
    Powiązania:
    https://bibliotekanauki.pl/articles/744903.pdf
    Data publikacji:
    2013
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    ordinary differential equation, nonlinear equation, Cauchy problem, initial value problem, fixed point, nonexpansive mapping, modular function space, Orlicz space, Musielak-Orlicz space, convex modular
    Opis:
    We consider ordinary differential equations \(u'(t)+(I-T)u(t)=0\), where an unknown function takes its values in a given modular function space being a generalization of Musielak-Orlicz spaces, and \(T\) is nonlinear mapping which is nonexpansive in the modular sense. We demonstrate that under certain natural assumptions the Cauchy problem related to this equation can be solved. We also show a process for the construction of such a solution. This result is then linked to the recent results of the fixed point theory in modular function spaces.
    Źródło:
    Commentationes Mathematicae; 2013, 53, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some analytical properties of the multidimensional continuous Mróz model of plasticity
    Autorzy:
    Brokate, M.
    Krejci, P.
    Rachinskij, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/206205.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    hartowanie kinetyczne
    operator histerezowy
    plastyczność
    hysteresis operator
    ill-posedness of Cauchy problem
    kinematic hardening
    Mróz model
    plasticity
    thermodynamic consistency
    Opis:
    We study the geometrical structure of memory induced by the continuous multidimensional Mróz model of plasticity. The results are used for proving the thermodynamic consistency of the model and composition and inversion formulas for input - memory state - output operators. We also show an example of nonuniqueness of solutions to a simple initial value problem involving the Mróz operator.
    Źródło:
    Control and Cybernetics; 1998, 27, 2; 199-215
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    General remarks on dynamic projection method
    Autorzy:
    Leble, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1938597.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Gdańska
    Tematy:
    partial differential equations
    dynamical system
    Cauchy problem
    diffusion equation
    projection operator
    idempotent operators
    eigen mode
    mode interaction
    boundary regime propagation
    Opis:
    A brief history and a mathematical description of the dynamic projection operators technique is presented. An example of the general Cauchy problem for evolution equations in 1+ 1 dimensions is studied in detail. A boundary regime propagation is formulated in terms of operators and illustrated by the simplest one-dimensional diffusion equation. The problem of temperature waves is discussed.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2016, 20, 2; 113-130
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An abstract Cauchy problem for higher order functional differential inclusions with infinite delay
    Autorzy:
    Ke, Tran
    Obukhovskii, Valeri
    Wong, Ngai-Ching
    Yao, Jen-Chih
    Powiązania:
    https://bibliotekanauki.pl/articles/729357.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Cauchy problem
    functional differential inclusion
    infinite delay
    higher order
    existence family
    phase space
    fixed point
    multivalued map
    measure of noncompactness
    condensing map
    Opis:
    The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 2; 199-229
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of solutions of the dynamic Cauchy problem on infinite time scale intervals
    Autorzy:
    Kubiaczyk, Ireneusz
    Sikorska-Nowak, Aneta
    Powiązania:
    https://bibliotekanauki.pl/articles/729401.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Cauchy dynamic problem
    Banach space
    measure of noncompactness
    Carathéodory's type solutions
    time scales
    fixed point
    Opis:
    In the paper, we prove the existence of solutions and Carathéodory's type solutions of the dynamic Cauchy problem
    $x^Δ(t) = f(t,x(t))$, t ∈ T,
    x(0) = x₀,
    where T denotes an unbounded time scale (a nonempty closed subset of R and such that there exists a sequence (xₙ) in T and xₙ → ∞) and f is continuous or satisfies Carathéodory's conditions and some conditions expressed in terms of measures of noncompactness. The Sadovskii fixed point theorem and Ambrosetti's lemma are used to prove the main result. The results presented in the paper are new not only for Banach valued functions, but also for real-valued functions.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2009, 29, 1; 113-126
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the numerical approximation of first-order Hamilton-Jacobi equations
    Autorzy:
    Abgrall, R.
    Perrier, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/929712.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    równanie Hamiltona-Jacobiego
    aproksymacja
    zagadnienie Cauchy'ego-Dirichleta
    siatka trójkątna
    approximation of Hamilton-Jacobi equations
    viscous solution
    Cauchy-Dirichlet problem
    triangular mesh
    Opis:
    Some methods for the numerical approximation of time-dependent and steady first-order Hamilton-Jacobi equations are reviewed. Most of the discussion focuses on conformal triangular-type meshes, but we show how to extend this to the most general meshes. We review some first-order monotone schemes and also high-order ones specially dedicated to steady problems.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 3; 403-412
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the existence for the Cauchy-Neumann problem for the Stokes system in the $L_p$-framework
    Autorzy:
    Mucha, Piotr
    Zajączkowski, Wojciech
    Powiązania:
    https://bibliotekanauki.pl/articles/1205939.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Stokes system
    Marcinkiewicz theorem
    Cauchy-Neumann initial boundary value problem
    the Fourier transform
    existence of solutions
    Opis:
    The existence for the Cauchy-Neumann problem for the Stokes system in a bounded domain $Ω ⊂ ℝ^3$ is proved in a class such that the velocity belongs to $W^{2,1}_r (Ω × (0,T))$, where r > 3. The proof is divided into three steps. First, the existence of solutions is proved in a half-space for vanishing initial data by applying the Marcinkiewicz multiplier theorem. Next, we prove the existence of weak solutions in a bounded domain and then we regularize them. Finally, the problem with nonvanishing initial data is considered.
    Źródło:
    Studia Mathematica; 2000, 143, 1; 75-101
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Metoda funkcji Cauchy w analizie częstości drgań kuli sprężystej
    Method of Cauchy function in analysis of radial vibration of an elastic sphere
    Autorzy:
    Jaroszewicz, J.
    Żur, K. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/209767.pdf
    Data publikacji:
    2012
    Wydawca:
    Wojskowa Akademia Techniczna im. Jarosława Dąbrowskiego
    Tematy:
    drgania promieniowe
    funkcja Cauchy'ego
    zagadnienie brzegowe
    radial vibrations
    Cauchy function
    boundary value problem
    Opis:
    W pracy zastosowano metodę funkcji Cauchy do rozwiązania zagadnienia brzegowego drgań promieniowych jednorodnej kuli sprężystej. Uwzględniono liniową zależność naprężenia, odkształcenia i przemieszczenia od promieniowej współrzędnej. Wyprowadzono analityczną postać szeregu charakterystycznego. Wykorzystując wzory i tablice Bernsteina-Kieropiana, obliczono częstości podstawowe i wyższe drgań promieniowych. Porównanie wyników obliczeń otrzymanych metodą funkcji wpływu z rozwiązaniem ścisłym potwierdza wysoką dokładność metody po uwzględnieniu kilku pierwszych członów szeregu charakterystycznego.
    In this study, the method of Cauchy function is applied to solve boundary-value problem of free radial vibrations of an elastic isotropic sphere. The linear dependence stress, deformation and displacement against radial coordinate are settled. The form of characteristic series was derived. The application of tables and formulas of Bernstein-Kieropian to calculate basic and higher estimators of radial vibration was presented. The presented method gives satisfactory accuracy to exact solution [5] even if the characteristic series is truncated after a few first terms.
    Źródło:
    Biuletyn Wojskowej Akademii Technicznej; 2012, 61, 4; 115-122
    1234-5865
    Pojawia się w:
    Biuletyn Wojskowej Akademii Technicznej
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Jan Stochel, a stellar mathematician
    Autorzy:
    Chavan, Sameer
    Curto, Raúl
    Jabłoński, Zenon Jan
    Jung, Il Bong
    Putinar, Mihai
    Powiązania:
    https://bibliotekanauki.pl/articles/29519747.pdf
    Data publikacji:
    2024
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    unbounded subnormal operator
    moment problem
    composition operator
    Cauchy dual
    Opis:
    The occasion for this survey article was the 70th birthday of Jan Stochel, professor at Jagiellonian University, former head of the Chair of Functional Analysis and a prominent member of the Kraków school of operator theory. In the course of his mathematical career, he has dealt, among other things, with various aspects of functional analysis, single and multivariable operator theory, the theory of moments, the theory of orthogonal polynomials, the theory of reproducing kernel Hilbert spaces, and mathematical aspects of quantum mechanics.
    Źródło:
    Opuscula Mathematica; 2024, 44, 3; 303-321
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Limitation of Cauchy function method in analysis for double estimators of free transversal vibration of cantilever tapered shafts
    Autorzy:
    Jaroszewicz, J.
    Dragun, Ł
    Powiązania:
    https://bibliotekanauki.pl/articles/298463.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Warmińsko-Mazurski w Olsztynie
    Tematy:
    cantilever shafts
    transversal
    vibrations
    Cauchy function
    boundary value problem
    Opis:
    In this paper the Bernstein-Kieropian simplest Dunkerly estimators of natural frequencies of cantilever shafts with power variable flexural rigidity and attached concentrated mass were analyzed in a theoretical approach. The approximate solution of boundary value problem of transversal vibrations by means of Cauchy function and characteristic series method has gave getting functional dependence between natural frequency and variable parameters of shafts. Particular attention has been given to a singularity arising from the uncertainty of estimates of Bernstein-Kieropian. Limitation of Cauchy function method in analysis double estimators of natural frequencies of transversal vibration of cantilever tapered shafts exude to exact theoretical selection using by Bessel’s function and experimental result received by Panuszka R., Uhl T.
    Źródło:
    Technical Sciences / University of Warmia and Mazury in Olsztyn; 2013, 16(2); 131-146
    1505-4675
    2083-4527
    Pojawia się w:
    Technical Sciences / University of Warmia and Mazury in Olsztyn
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of the influence of elasticity constants and material density on the base frequency of axi-symmetrical vibrations with variable thickness plates
    Analiza wpływu stałych sprężystych i gęstości materiału na częstość podstawową drgań osiowosymetrycznych płyt kołowych o zmiennej grubości
    Autorzy:
    Domoradzki, M.
    Jaroszewicz, J.
    Zoryj, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/279707.pdf
    Data publikacji:
    2005
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    circular plates
    variable thickness
    boundary value problem
    Cauchy function method
    Opis:
    In the paper, the influence of Young's modulus and Poisson ratio as well as mass density of a material on the base frequency of circular plates of the diaphragm type with variable thickness is discussed. In order to solve the boundary-value problem, the Cauchy function method and double Bernstein-Kieropian estimators were applied. An analytical form of Cauchy's influence function was found and used to construct the characteristic equation in the form of a power series with respect to a frequency parameter. Application of this method allowed a functional dependency of the base frequency on material constants of the plates to be established. The results of calculations for plates made of duralumin and tin were mentioned as examples. Comparison of the obtained results with those found in scientific literature indicated high accuracy of the method applied therein.
    W pracy zbadano wpływ modułu sprężystości Younga i liczby Poissona, a także gęstości materiału na częstość podstawową płyt o zmiennej grubości typu diafragmy i dysku. Do rozwiązania zagadnienia brzegowego zastosowano metodę funkcji wpływu Cauchy, najprostszy estimator z niedostatkiem i dwustronne estymatory Bernstejna-Kieropiana. Znaleziono analityczną postać funkcji wpływu Cauchy, z pomocą której zbudowano równanie charakterystyczne w postaci szeregu potęgowego względem parametru częstotliwości. Zastosowanie metody pozwoliło wyprowadzić funkcjonalną zależność częstości podstawowej od stałych materiałowych wymienionych płyt. W charakterze przykładu przytoczono wyniki obliczeń dla płyt wykonanych z duraluminium i z cyny. Porównanie wyników obliczen ze znanymi z literatury potwierdziły wysoką dokładność metody.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2005, 43, 4; 763-775
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of natural frequency of flexural vibrations of a single-span beam with the consideration of Timoshenko effect
    Autorzy:
    Jaroszewicz, J.
    Łukaszewicz, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/950070.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Warmińsko-Mazurski w Olsztynie
    Tematy:
    beam
    boundary value problem
    transversal vibration
    Timoshenko effect
    FEM
    Cauchy function
    characteristic series methods
    Opis:
    This paper presents general solution of boundary value problem for constant cross-section Timoshenko beams with four typical boundary conditions. The authors have taken into consideration rotational inertia and shear strain by using the theory of influence by Cauchy function and characteristic series. The boundary value problem of transverse vibration has been formulated and solved. The characteristic equations considering the exact bending theory have been obtained for four cases: the clamped boundary conditions; a simply supported beam and clamped on the other side; a simply supported beam; a cantilever beam. The obtained estimators of fundamental natural frequency take into account mass and elastic characteristics of beams and Timoshenko effect. The results of calculations prove high convergence of the estimators to the exact values which were calculated by Timoshenko who used Bessel functions. Characteristic series having an alternating sign power series show good convergence. As it is shown in the paper, the error lower than 5% was obtained after taking into account only two first significant terms of the series. It was proved that neglecting the Timoshenko effect in case of short beams of rectangular section with the ratio of their length to their height equal 6 leads to the errors of calculated natural frequency: 5%÷12%.
    Źródło:
    Technical Sciences / University of Warmia and Mazury in Olsztyn; 2018, 21(3); 215-232
    1505-4675
    2083-4527
    Pojawia się w:
    Technical Sciences / University of Warmia and Mazury in Olsztyn
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The general formula for calculation of fundamental frequency of axisymmetric vibrations of circular plates with linearly variable thickness
    Autorzy:
    Jaroszewicz, J.
    Radziszewski, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/297898.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Warmińsko-Mazurski w Olsztynie
    Tematy:
    circular plates
    variable thickness
    boundary value problem
    Cauchy function method
    simple estimator of fundamental frequency
    Opis:
    This work has derived the general formula, sufficiently precise for engineering calculations of base frequency of axisymmetric free vibrations of uniform, circular diaphragm type plates clamped at the edge with linearly variable thickness. To solve the boundary problem, the Cauchy’s function method and characteristic series have been applied. The above formula has been derived on the basis of Dunkerley’s formula which is based on the first major term of the characteristic series and results in the simplest, lower bound estimator. The analysis of the formula shows that the base frequency coefficient for diaphragm plates clamped at the edge depends to only a small extent on the Poisson’s ratio, and therefore it may be averaged in the case of construction materials. Comparison of the calculations results of the simplest lower bound estimators for the base frequency obtained by using proposed method, with the results known from the literature as precise solutions, including Conway method, confirmed the high accuracy of the proposed method.
    Źródło:
    Technical Sciences / University of Warmia and Mazury in Olsztyn; 2016, 19(4); 401-410
    1505-4675
    2083-4527
    Pojawia się w:
    Technical Sciences / University of Warmia and Mazury in Olsztyn
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Limitation of Cauchy Function Method in Analysis of Estimators of Frequency and Form of Natural Vibrations of Circular Plate with Variable Thickness and Clamped Edges
    Autorzy:
    Jaroszewicz, J.
    Żur, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/387099.pdf
    Data publikacji:
    2012
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    drgania
    model płaskiej struktury
    zagadnienia brzegowe
    estymatory Bernsteina-Kieropiana
    vibration
    circular plate
    boundary value problem
    Cauchy function
    Bernstein-Kieropian’s estimators
    Opis:
    In this paper the Berstein-Kieropian double estimators of basic natural frequency of circular plate with power variable thickness along the radius and clamped edges in diaphragm form were analyzed in a theoretical approach. The approximate solution of boundary problem of transversal vibration by means of Cauchy function and characteristic series method has been applied for chosen values of power indicator of variable thickness and material Poisson’s ratio has been chosen which led to exact form solutions. Particular attention has been given to a singularity arising from the uncertainty of estimates of Bernstein-Kieropian. Improving this method has been obtained the general form of Cauchy function for arbitrary values of and , which are physically justified. Therefore, the aim of the paper was to explore the reason why for a plate above a certain value = 3.97 exact solution, which Conway couldn’t receive (Conway, 1958a, b)
    Źródło:
    Acta Mechanica et Automatica; 2012, 6, 2; 53-57
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-40 z 40

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