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    Wyświetlanie 1-14 z 14
    Tytuł:
    Exact difference schemes and schemes of higher order of approximation for convection-diffusion equation. I
    Autorzy:
    Lapinska-Chrzczonowicz, M.
    Matus, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/106186.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    convection-diffusion equation
    initial-boundary value problem
    traveling wave
    EDS
    Opis:
    The initial-boundary value problem for a convection-diffusion equation [formula] is considered. The difference scheme, approximating this problem, is constructed. It is shown that for traveling wave solutions the scheme is exact (EDS). The monotonicity of the scheme is also taken into consideration. Presented numerical experiments illustrate the theoretical results investigated in the paper.
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica; 2013, 13, 1; 37-51
    1732-1360
    2083-3628
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica
    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:
    Matrix Greens function of double-diffusivity problem and its applications to problems with inner point source
    Autorzy:
    Chaplya, Yevhen
    Chernukha, Olha
    Bilushchak, Yurii
    Powiązania:
    https://bibliotekanauki.pl/articles/1954454.pdf
    Data publikacji:
    2014
    Wydawca:
    Politechnika Gdańska
    Tematy:
    Green’s function
    double-diffusivity
    initial-boundary value problem
    point mass source
    random coordinate
    Opis:
    The matrix Green’s function of the initial-boundary value problem of admixture double-diffusivity is defined. The initial-boundary value problem with a point source is formulated for the matrix elements for determination of the matrix Green’s function. Formulae for matrix elements are obtained and the behavior of Green’s functions is investigated. It is shown that the surface generated by the Green’s function has a typical sharp peak in the vicinity of the point of action of the point mass source, and in the vicinity of the top boundary of the layer ,the values of the second element of the Green’s function are times higher than the values of the first one the state of which is corresponding to the quick migration way. On this basis the solutions of the initial-boundary value problems under the action of the internal point source of mass are found. The cases of the deterministic source as well as stochastic ones under uniformand triangular distributions of the coordinate of the mass source location are considered.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2019, 23, 1; 75-99
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    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 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 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:
    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
    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:
    Entropy generation minimization in transient heat conduction processes PART II – Transient heat conduction in solids
    Autorzy:
    Kolenda, Z. S.
    Szmyd, J. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/201936.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    transient heat conduction
    initial boundary value problem
    entropy generation minimization
    przewodzenia ciepła
    początkowa wartość graniczna
    minimalizacja entropii generacji
    Opis:
    Formulation and solution of the initial boundary-value problem of heat conduction in solids have been presented when an entropy generation minimization principle is imposed as the arbitrary constraint. Using an entropy balance equation and the Euler-Lagrange variational approach a new form of the heat conduction equation (non-linear partial difference equation) is derived.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 4; 883-887
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    K-dron, jego matematyczne modelowanie i zastosowanie
    K-dron, its mathematical modelling and applications
    Autorzy:
    Kapusta, J.
    Gawinecki, J.
    Łazuka, J.
    Rafa, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/210273.pdf
    Data publikacji:
    2016
    Wydawca:
    Wojskowa Akademia Techniczna im. Jarosława Dąbrowskiego
    Tematy:
    K-dron
    transformata Laplace'a
    równanie drgań struny
    zagadnienie brzegowo-początkowe
    Laplace'a transform
    partial differential of string equation of vibration
    initial-boundary value problem
    Opis:
    W pracy przedstawiono pojęcie K-dronu, nowego kształtu geometrycznego odkrytego w 1985 roku w Nowym Jorku przez dr. Janusza Kapustę, historię jego odkrycia, związki z geometrią, symetrią sześcianu. Należy podkreślić, że autorzy wyprowadzili nowy wzór na powierzchnie K-dronu, stosując metodę transformacji Laplace’a do wyznaczenia rozwiązania zagadnienia brzegowo-początkowego do równania drgań struny. Wyprowadzony wzór w swojej naturze jest bardziej czytelny ze wzlgędu na swoją strukturę. Otrzymane przez autorów w pracy rozwiązanie opisuje w sposób najbardziej ogólny powierzchnie K-dronu oraz bardziej ogólne powierzchnie nazwane przez autorów n-K-dronem. Wzór na powierzchnie K-dronu uzyskany metodą transformaty Laplace’a posiada przejrzystą interpretację geometryczną, ponieważ jest przedstawiony w postaci kombinacji liniowej równań płaszczyzn o współczynnikach kierunkowych określonych przez odpowiednie kombinacje funkcje Heaviside’a. Szeroko także przedstawiono różnorodne i wielorakie zastosowanie K-dronu.
    In this paper we present the definition of K-dron, new geometrical form discovered by Janusz Kapusta in 1985 in New York, its history and connection between geometry and symmetry of a cube. It is worth to emphasize that the authors have derived new formulae for the surface of K-dron using the Laplacea transform in order to obtain the solution of the boundary-value problem for the partial differential equation describing the vibration of the string. The formula proved by us in this paper is clearer and understandable in view of this structure. The solution obtained in this paper describes in general manner the surface of K-dron and more general surfaces named by us n-K-drons. The formula for the surface of K-dron was derived by the method of Laplacea transform having clear geometrical and physical interpretation because it is presented in linear combination of the equation of planes with the coefficients of directions described by suitable combinations of Heavisides functions. Also wide range and different applications of K-dron are presented.
    Źródło:
    Biuletyn Wojskowej Akademii Technicznej; 2016, 65, 1; 169-202
    1234-5865
    Pojawia się w:
    Biuletyn Wojskowej Akademii Technicznej
    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:
    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:
    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:
    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
      Wyświetlanie 1-14 z 14

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