Discrete Dynamics in Nature and Society
Volume 2004 (2004), Issue 2, Pages 273-286
doi:10.1155/S1026022604403033
On well-posedness of the nonlocal boundary value problem for parabolic difference equations
1Department of Mathematics, Fatih University, 34900 Büyükçekmece, Istanbul, Turkey
2Department of Applied Mathematics, International Turkmen-Turkish University, 32 Gerogly Street, Ashgabat 74400, Turkmenistan
3Department of Mathematics, Yildiz Technical University, Davutpasa Campus, 34210 Esenler, Istanbul, Turkey
4Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel
Received 21 March 2004
Copyright © 2004 A. Ashyralyev et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We consider the nonlocal boundary value problem for difference
equations (uk−uk−1)/τ+Auk=φk, 1≤k≤N, Nτ=1, and u0=u[λ/τ]+φ, 0<λ≤1, in an
arbitrary Banach space E with the strongly positive operator
A. 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.