Well-Posedness of the Boundary Value Problem for  Parabolic Equations in Difference Analogues of Spaces  of Smooth Functions

Ashyralyev, A.

doi:https://doi.org/10.1155/2007/90815

Mathematical Problems in Engineering

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Research Article | Open Access

Volume 2007 | Article ID 090815 | https://doi.org/10.1155/2007/90815

Well-Posedness of the Boundary Value Problem for Parabolic Equations in Difference Analogues of Spaces of Smooth Functions

A. Ashyralyev¹

Academic Editor: F. E. Udwadia

Received15 Jun 2006

Accepted27 Dec 2006

Published08 Mar 2007

Abstract

The first and second orders of accuracy difference schemes for the approximate solutions of the nonlocal boundary value problem v′(t)+Av(t)=f(t) (0≤t≤1), v(0)=v(λ)+μ, 0<λ≤1, for differential equation in an arbitrary Banach space E with the strongly positive operator A are considered. The well-posedness of these difference schemes in difference analogues of spaces of smooth functions is established. In applications, the coercive stability estimates for the solutions of difference schemes for the approximate solutions of the nonlocal boundary value problem for parabolic equation are obtained.

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Copyright

Copyright © 2007 A. Ashyralyev. 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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