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Wyszukujesz frazę "initial value problem" wg kryterium: Temat


Tytuł:
Some closed-form bending formulas for elastically restrained Euler-Bernoulli beams under point and uniformly distributed loads
Autorzy:
Yıldırım, V.
Powiązania:
https://bibliotekanauki.pl/articles/122937.pdf
Data publikacji:
2018
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Euler-Bernoulli beam
elastic support
transfer matrix method
initial value problem
bending
belka Eulera-Bernoulliego
teoria Eulera-Bernoulliego
metoda macierzy transferu
Opis:
The transfer matrix method based on the Euler-Bernoulli beam theory is employed in order to originally achieve some exact analytical formulas for elastically supported beams under a point force together with uniformly distributed force and uniformly distributed couple moments. Those closed-form formulas can be used in a variety of engineering applications especially at the pre-design stage to get an insight into the response of the structure. Contrary to the classical boundary conditions, it is also observed that the Euler-Bernoulli solutions of a beam with elastic supports are sensitive to the ratio of length to thickness (L/h).
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 3; 97-109
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On strongly monotone flows
Autorzy:
Walter, Wolfgang
Powiązania:
https://bibliotekanauki.pl/articles/1294817.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
system of ordinary differential equations
initial value problem
comparison theorem
monotone flow
quasimonotonicity
Opis:
M. Hirsch's famous theorem on strongly monotone flows generated by autonomous systems u'(t) = f(u(t)) is generalized to the case where f depends also on t, satisfies Carathéodory hypotheses and is only locally Lipschitz continuous in u. The main result is a corresponding Comparison Theorem, where f(t,u) is quasimonotone increasing in u; it describes precisely for which components equality or strict inequality holds.
Źródło:
Annales Polonici Mathematici; 1997, 66, 1; 269-274
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The evolution of linearized perturbations in a magnetohydrodynamic boundary layer
Autorzy:
Vijayalakshmi, A. R.
Balagondar, P. M.
Powiązania:
https://bibliotekanauki.pl/articles/955146.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
magnetohydrodynamika
transformacja Fouriera
warstwa graniczna
pole magnatyczne
magnetohydrodynamic boundary layer
initial-value problem approach
Alfv’n velocity
Fourire transform technique
Opis:
The evolution of linearized perturbations in a magnetohydrodynamic shear flow is studied using the initial value problem approach. Here the resulting equation in time posed by using the Fourier transform is solved for the Fourier amplitudes for modeled boundary layer for different initial disturbances. The shear flow prototype here is a piecewise linear approximation of a magnetohydrodynamic boundary layer. The initial disturbances that are considered are a point source of the field of transverse velocity and magnetic field. Solutions are obtained for small values of Alfve’n velocity. The velocity plots are drawn for different values of Alfve’n velocity.
Źródło:
International Journal of Applied Mechanics and Engineering; 2014, 19, 2; 397-406
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Long-time asymptotics for the nonlinear heat equation with a fractional Laplacian in a ball
Autorzy:
Varlamov, Vladimir
Powiązania:
https://bibliotekanauki.pl/articles/1206006.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
first initial-boundary value problem
nonlinear heat equation
construction of solutions
higher-order long-time asymptotics
fractional Laplacian
Opis:
The nonlinear heat equation with a fractional Laplacian $[u_t+(-Δ)^{α/2} u = u^2, 0 < α ≤ 2]$, is considered in a unit ball $B$. Homogeneous boundary conditions and small initial conditions are examined. For 3/2 + ε₁ ≤ α ≤ 2, where ε₁ > 0 is small, the global-in-time mild solution from the space $C⁰([0,∞), H₀^{κ}(B))$ with κ < α - 1/2 is constructed in the form of an eigenfunction expansion series. The uniqueness is proved for 0 < κ < α - 1/2, and the higher-order long-time asymptotics is calculated.
Źródło:
Studia Mathematica; 2000, 142, 1; 71-99
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear Heat Equation with a Fractional Laplacian in a Disk
Autorzy:
Varlamov, Vladimir
Powiązania:
https://bibliotekanauki.pl/articles/965893.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
nonlinear heat equation
long-time asymptotics
fractional Laplacian
initial-boundary value problem in a disk
Opis:
For the nonlinear heat equation with a fractional Laplacian $u_t + (-Δ)^{α/2} u = u^2$, 1 < α ≤ 2, the first initial-boundary value problem in a disk is considered. Small initial conditions, homogeneous boundary conditions, and periodicity conditions in the angular coordinate are imposed. Existence and uniqueness of a global-in-time solution is proved, and the solution is constructed in the form of a series of eigenfunctions of the Laplace operator in the disk. First-order long-time asymptotics of the solution is obtained.
Źródło:
Colloquium Mathematicum; 1999, 81, 1; 101-122
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Kuramoto-Sivashinsky equation in a disk
Autorzy:
Varlamov, Vladimir
Powiązania:
https://bibliotekanauki.pl/articles/1208011.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
first initial-boundary value problem
long-time asymptotics
Kuramoto-Sivashinsky equation
disk
Opis:
We consider the first initial-boundary value problem for the 2-D Kuramoto-Sivashinsky equation in a unit disk with homogeneous boundary conditions, periodicity conditions in the angle, and small initial data. Apart from proving the existence and uniqueness of a global in time solution, we construct it in the form of a series in a small parameter present in the initial conditions. In the stable case we also obtain the uniform in space long-time asymptotic expansion of the constructed solution and its asymptotics with respect to the nonlinearity constant. The method can work for other dissipative parabolic equations with dispersion.
Źródło:
Annales Polonici Mathematici; 2000, 73, 3; 227-256
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Flow-induced Vibrations of a Horizontal Elastic Band Plate Submerged in Fluid of Finite Depth
Autorzy:
Szmidt, Kazimierz
Hedzielski, Benedykt
Powiązania:
https://bibliotekanauki.pl/articles/241049.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
Tematy:
elastic plate vibrations
surface waves
initial value problem
coupled problem
Opis:
The paper deals with forced vibrations of a horizontal thin elastic plate submerged in a semi-infinite layer of fluid of constant depth. The pressure load on this plate is induced by water waves arriving at the plate. This load is accompanied by pressure resulting from the motion of the plate. The plate and fluid motions depend on boundary conditions, and, in particular, the pressure load depends on the width of the gap between the plate and the bottom. In theoretical description of the phenomenon, we deal with a coupled problem of hydrodynamics in which the plate and fluid motions are coupled through boundary conditions at the plate surfaces. The main attention is focused on transient solutions of the problem, which correspond to fluid (and plate) motion starting from rest. In formulation of this problem, a linear theory of small deflections of the plate is employed. In order to calculate the fluid pressure, a solution of Laplace’s equation is constructed in a doubly connected fluid domain. With respect to the initial value problem considered, we confine our attention to a finite fluid domain. For a finite elapse of time, measured from the starting point, the solution in the finite fluid area mimics a solution within an infinite domain, inherent for wave propagation problems. Because of the complicated structure of boundary conditions of the coupled problem considered, the fluid domain is divided into sub-domains of simple geometry, and the solutions of the problem equations are constructed separately in each of these domains. Numerical experiments have been conducted to illustrate the formulation developed in this paper.
Źródło:
Archives of Hydro-Engineering and Environmental Mechanics; 2019, 66, 3-4; 101-130
1231-3726
Pojawia się w:
Archives of Hydro-Engineering and Environmental Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Local existence of solutions of the mixed problem for the system of equations of ideal relativistic hydrodynamics
Autorzy:
Rencławowicz, Joanna
Zajączkowski, Wojciech
Powiązania:
https://bibliotekanauki.pl/articles/1339037.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
relativistic hydrodynamics
symmetrization
existence
system of hyperbolic equations of the first order
initial-boundary value problem
Opis:
Existence and uniqueness of local solutions for the initial-boundary value problem for the equations of an ideal relativistic fluid are proved. Both barotropic and nonbarotropic motions are considered. Existence for the linearized problem is shown by transforming the equations to a symmetric system and showing the existence of weak solutions; next, the appropriate regularity is obtained by applying Friedrich's mollifiers technique. Finally, existence for the nonlinear problem is proved by the method of successive approximations.
Źródło:
Applicationes Mathematicae; 1998-1999, 25, 2; 221-252
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the use of Mohand integral transform for solving fractional-order classical Caputo differential equations
Autorzy:
Qureshi, Sania
Yusuf, Abdullahi
Aziz, Shaheen
Powiązania:
https://bibliotekanauki.pl/articles/1839755.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
initial value problem
kinetic reaction
Riemann-Liouville integral
transformata całkowa Mohanda
całka Mohanda
całka Riemanna-Liouville'a
reakcja kinetyczna
Opis:
In this research study, a newly devised integral transform called the Mohand transform has been used to find the exact solutions of fractional-order ordinary differential equations under the Caputo type operator. This transform technique has successfully been employed in existing literature to solve classical ordinary differential equations. Here, a few significant and practically-used differential equations of the fractional type, particularly related with kinetic reactions from chemical engineering, are under consideration for the possible outcomes via the Mohand integral transform. A new theorem has been proposed whose proof, provided in the present study, helped to get the exact solutions of the models under investigation. Upon comparison, the obtained results would agree with results produced by other existing well-known integral transforms including Laplace, Fourier, Mellin, Natural, Sumudu, Elzaki, Shehu and Aboodh.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 3; 99-109
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fourier-like methods for equations with separable variables
Autorzy:
Przeworska-Rolewicz, Danuta
Powiązania:
https://bibliotekanauki.pl/articles/729392.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
algebraic analysis
commutative algebra with unit
Leibniz condition
logarithmic mapping
antilogarithmic mapping
right invertible operator
sine mapping
cosine mapping
initial value problem
boundary value problem
Fourier method
Opis:
It is well known that a power of a right invertible operator is again right invertible, as well as a polynomial in a right invertible operator under appropriate assumptions. However, a linear combination of right invertible operators (in particular, their sum and/or difference) in general is not right invertible. It will be shown how to solve equations with linear combinations of right invertible operators in commutative algebras using properties of logarithmic and antilogarithmic mappings. The used method is, in a sense, a kind of the variables separation method. We shall obtain also an analogue of the classical Fourier method for partial differential equations. Note that the results concerning the Fourier method are proved under weaker assumptions than these obtained in [6] (cf. also [7, 8, 11]).
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2009, 29, 1; 19-42
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An intial-value technique for self-adjoint singularly perturbed two-point boundary value problems
Autorzy:
Padmaja, P.
Aparna, P.
Gorla, R. S. R.
Powiązania:
https://bibliotekanauki.pl/articles/264933.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
wartość początkowa
wartość brzegowa
perturbacja procesu
initial value technique
boundary value problem
singular perturbation problem
Opis:
In this paper, we present an initial value technique for solving self-adjoint singularly perturbed linearvboundary value problems. The original problem is reduced to its normal form and the reduced problem is converted to first order initial value problems. This replacement is significant from the computational point of view. The classical fourth order Runge-Kutta method is used to solve these initial value problems. This approach to solve singularly perturbed boundary-value problems is numerically very appealing. To demonstrate the applicability of this method, we have applied it on several linear examples with left-end boundary layer and rightend layer. From the numerical results, the method seems accurate and solutions to problems with extremely thin boundary layers are obtained.
Źródło:
International Journal of Applied Mechanics and Engineering; 2020, 25, 1; 106-126
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems
Autorzy:
Navarro, Enrique
Company, Rafael
Jódar, Lucas
Powiązania:
https://bibliotekanauki.pl/articles/1340656.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
initial value problem
closed form solution
fundamental set
boundary value problem
Bessel matrix equation
Opis:
In this paper we consider Bessel equations of the type $t^2 X^{(2)}(t) + t X^{(1)}(t) + (t^2 I - A^2)X(t) = 0$, where A is an n$\times$n complex matrix and X(t) is an n$\times$m matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.
Źródło:
Applicationes Mathematicae; 1993-1995, 22, 1; 11-23
1233-7234
Pojawia się w:
Applicationes Mathematicae
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:
Local controllability of nonlinear discrete-time fractional order systems
Autorzy:
Mozyrska, D.
Pawłuszewicz, E.
Powiązania:
https://bibliotekanauki.pl/articles/201944.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional difference operator
fractional difference initial value problem
nonlinear fractional order system
linear approximation
controllability problem
Opis:
The Riemann-Liouville, Caputo and Gr¨unwald-Letnikov fractional order difference operators are discussed and used to state and solve the controllability problem of a nonlinear fractional order discrete-time system. It is shown that independently of the type of fractional order difference, such a system is locally controllable in q steps if its linear approximation is globally controllable in q steps.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 1; 251-256
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solution of fractional heat-like and fractional wave-like equation by using modern strategy
Autorzy:
Mohamed, Zain El Abden
Hamza, Amjad
Elzaki, Tarig
Algolam, Mohamed
Elhussein, Shiraz
Powiązania:
https://bibliotekanauki.pl/articles/2233715.pdf
Data publikacji:
2023
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
fractional-order wave-like equation
fractional-order heat-like equation
initial-boundary value problem
Adomian decomposition method
Opis:
This paper introduces a novel form of the Adomian decomposition (ADM) method for solving fractional-order heat-like and wave-like equations with starting and boundary value problems. The derivations are provided in the sense of Caputo. In order to help understanding, the generalised formulation of the current approach is provided. Several numerical examples of fractional-order diffusion-wave equations (FDWEs) are solved using the suggested method in this context. In addition to examining the applicability of the suggested method to the solving of fractional-order heat-like and wave-like equations, a graphical depiction of the solutions to three instructive cases was constructed. Solution graphs were arrived at for integer and fractional-order problems. The derived and exact solutions to integer-order problems were found to be in excellent agreement. The subject of the present research endeavour is the convergence of fractional-order solutions. This strategy is considered to be the most successful way of addressing fractional-order initial-boundary value issues in science and engineering. This strategy is presented here.
Źródło:
Acta Mechanica et Automatica; 2023, 17, 3; 372--380
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł

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