On well-posedness of the nonlocal boundary value problem for parabolic difference equations-Reference-Cited by-同舟云学术

On well-posedness of the nonlocal boundary value problem for parabolic difference equations

Published:2004 Issue:2 Volume:2004 Page:273-286
ISSN:1026-0226
Container-title:Discrete Dynamics in Nature and Society
language:en
Short-container-title:Discrete Dynamics in Nature and Society

Author:

Ashyralyev A.¹²,Karatay I.¹³,Sobolevskii P. E.⁴

Affiliation:

1. Department of Mathematics, Fatih University, 34900 Büyükçekmece, Istanbul, Turkey

2. Department of Applied Mathematics, International Turkmen-Turkish University, 32 Gerogly Street, Ashgabat 74400, Turkmenistan

3. Department of Mathematics, Yildiz Technical University, Davutpasa Campus, 34210 Esenler, Istanbul, Turkey

4. Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel

Abstract

We consider the nonlocal boundary value problem for difference equations(uk−uk−1)/τ+Auk=φk,1≤k≤N,Nτ=1, andu0=u[λ/τ]+φ,0<λ≤1, in an arbitrary Banach spaceEwith the strongly positive operatorA. The well-posedness of this nonlocal boundary value problem for difference equations in various Banach spaces is studied. In applications, the stability and coercive stability estimates in Hölder norms for the solutions of the difference scheme of the mixed-type boundary value problems for the parabolic equations are obtained. Some results of numerical experiments are given.

Publisher

Hindawi Limited

Subject

Modelling and Simulation

Link

http://downloads.hindawi.com/journals/ddns/2004/725979.pdf

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