Abstract and Applied Analysis

The Difference Problem of Obtaining the Parameter of a Parabolic Equation

Charyyar Ashyralyyev and Oznur Demirdag

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Abstract

The boundary value problem of determining the parameter p of a parabolic equation υ ( t ) + A υ ( t ) = f ( t ) + p   ( 0 t 1 ) ,   υ ( 0 ) = φ ,   υ ( 1 ) = ψ in an arbitrary Banach space E with the strongly positive operator A is considered. The first order of accuracy stable difference scheme for the approximate solution of this problemis investigated. The well-posedness of this difference scheme is established. Applying the abstract result, the stability and almost coercive stability estimates for the solution of difference schemes for the approximate solution of differential equations with parameter are obtained.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 603018, 14 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365174052

Digital Object Identifier
doi:10.1155/2012/603018

Mathematical Reviews number (MathSciNet)
MR2947682

Zentralblatt MATH identifier
1250.35180

Citation

Ashyralyyev, Charyyar; Demirdag, Oznur. The Difference Problem of Obtaining the Parameter of a Parabolic Equation. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 603018, 14 pages. doi:10.1155/2012/603018. https://projecteuclid.org/euclid.aaa/1365174052


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