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
A. Ashyralyev1
, I. Karatay1
and P.E. Sobolevskii3
1Department of Mathematics, Fatih University, 34900 Büyükçekmece, Istanbul, Turkey
3Institute 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, 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.