Discrete Dynamics in Nature and Society

Discrete Dynamics in Nature and Society / 2004 / Article

Open Access

Volume 2004 |Article ID 725979 | https://doi.org/10.1155/S1026022604403033

A. Ashyralyev, I. Karatay, P. E. Sobolevskii, "On well-posedness of the nonlocal boundary value problem for parabolic difference equations", Discrete Dynamics in Nature and Society, vol. 2004, Article ID 725979, 14 pages, 2004. https://doi.org/10.1155/S1026022604403033

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

Received21 Mar 2004

Abstract

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.

Copyright © 2004 Hindawi Publishing Corporation. 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.


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