On well-posedness of the nonlocal boundary value problem for parabolic difference equations
type: Item
instance of: scholarly article
title: On well-posedness of the nonlocal boundary value problem for parabolic difference equations
zbMATH Open document ID: 1077.39015
DOI: 10.1155/S1026022604403033
published in: Discrete Dynamics in Nature and Society
publication date: 2005-04-22T00:00:00Z
full work available at URL: https://eudml.org/doc/125387
review text: In an arbitrary Banach space, the authors consider a nonlocal boundary value problem for the difference equation \[ \frac{u_k - u_{k-1}}{\tau} + A u_k = \varphi_k, \;1 \leq k \leq N, \;N\tau = 1, \;u_0 = u_{[\lambda/\tau]} + \varphi, \tag{1} \] where \(A\) is a strongly positive operator. Stability and coercive stability of (1) in various Banach spaces are studied. As applications, difference schemes of boundary-value problems for parabolic equations are considered.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 47B39
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 2160814
zbMATH Keywords: difference equation
zbMATH Keywords: nonlocal boundary value problem
zbMATH Keywords: parabolic equation
zbMATH Keywords: stability
zbMATH Keywords: Banach space
author: Allaberen Ashyralyev
author: İbrahim Karatay
author: P. E. Sobolevskii
reviewed by: Victor I. Tkachenko
MaRDI profile type: Publication
OpenAlex ID: W2054697003
description: scientific article; zbMATH DE number 2160814