Temat: infinite systems of parabolic differential-functional equations - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations
Autorzy:: Brzychczy, Stanisław
Powiązania:: https://bibliotekanauki.pl/articles/1293995.pdf
Data publikacji:: 1999
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: method of lower and upper functions
infinite systems of parabolic differential-functional equations
monotone iterative method
Opis:: We consider the Fourier first boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations. To prove the existence and uniqueness of solution, we apply a monotone iterative method using J. Szarski's results on differential-functional inequalities and a comparison theorem for infinite systems.
Źródło:: Annales Polonici Mathematici; 1999, 72, 1; 15-24
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type
Autorzy:: Zabawa, T.S.
Powiązania:: https://bibliotekanauki.pl/articles/254967.pdf
Data publikacji:: 2006
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: stability of solutions
infinite systems
parabolic equations
elliptic equations
semilinear differential-functional equations
monotone iteration method
Opis:: A parabolic initial boundary value problem and an associated elliptic Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations are considered. It is shown that the solutions of the parabolic problem is asymptotically stable and the limit of the solution of the parabolic problem as t → ∞ is the solution of the associated elliptic problem. The result is based on the monotone methods.
Źródło:: Opuscula Mathematica; 2006, 26, 1; 173-183
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Difference problems generated by infinite systems of nonlinear parabolic functional differential equations with the Robin conditions
Autorzy:: Czernous, W.
Jaruszewska-Walczak, D.
Powiązania:: https://bibliotekanauki.pl/articles/255694.pdf
Data publikacji:: 2014
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: nonlinear parabolic equations
functional differential equations
infinite systems
Volterra type operators
nonlinear estimates of Perron type
truncation methods
Opis:: We consider the classical solutions of mixed problems for infinite, countable systems of parabolic functional differential equations. Difference methods of two types are constructed and convergence theorems are proved. In the first type, we approximate the exact solutions by solutions of infinite difference systems. Methods of second type are truncation of the infinite difference system, so that the resulting difference problem is finite and practically solvable. The proof of stability is based on a comparison technique with nonlinear estimates of the Perron type for the given functions. The comparison system is infinite. Parabolic problems with deviated variables and integro-differential problems can be obtained from the general model by specifying the given operators.
Źródło:: Opuscula Mathematica; 2014, 34, 2; 311-326
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Monotone iterative methods for infinite systems of reaction-diffusion-convection equations with functional dependence
Autorzy:: Brzychczy, S.
Powiązania:: https://bibliotekanauki.pl/articles/255097.pdf
Data publikacji:: 2005
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: infinite systems
reaction-diffusion-convection equations
semilinear parabolic differential-functional equations
Volterra functionals
monotone iterative methods
method of upper and lower solutions
Opis:: We consider the Fourier first initial-boundary value problem for an infinite system of semilinear parabolic differential-functional equations of reaction-diffusion-convection type of the form [formula] where [formula] in a bounded cylindrical domain (0, T] x G := D rcup Rm+1. The right-hand sides of the system are Volterra type functionals of the unknown function z. In the paper, we give methods of the construction of the monotone iterative sequences converging to the unique classical solution of the problem considered in partially ordered Banach spaces with various convergence rates of iterations. We also give remarks on monotone iterative methods in connection with numerical methods, remarks on methods for the construction of lower and upper solutions and remarks concerning the possibility of extending these methods to more general parabolic equations. All monotone iterative methods are based on differential inequalities and, in this paper, we use the theorem on weak partial differential-functional inequalities for infinite systems of parabolic equations, the comparison theorem and the maximum principle. A part of the paper is based on the results of our previous papers. These results generalize the results obtained by several authors in numerous papers for finite systems of semilinear parabolic differential equations to encompass the case of infinite systems of semilinear parabolic differential-functional equations. The monotone iterative schemes can be used for the computation of numerical solutions.
Źródło:: Opuscula Mathematica; 2005, 25, 1; 29-99
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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