Discrete Dynamics in Nature and Society
Volume 2004 (2004), Issue 2, Pages 273-286

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

A. Ashyralyev,1,2 I. Karatay,1,3 and P. E. Sobolevskii4

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.


We consider the nonlocal boundary value problem for difference equations (ukuk1)/τ+Auk=φk, 1kN, Nτ=1, and u0=u[λ/τ]+φ, 0<λ1, 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.