A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems

A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems

We study a final value problem for first-order abstract differential equation with positive self-adjoint unbounded operator coefficient. This problem is ill-posed. Perturbing the final condition, we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate p...

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Main Authors: S. Djezzar, M. Denche
Format: Article
Language:English
Published: SpringerOpen 2006-02-01
Series:Boundary Value Problems
Online Access:http://dx.doi.org/10.1155/BVP/2006/37524
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spelling doaj-0b513d35846c40e499d02ac9955d53a62020-11-24T21:18:28ZengSpringerOpenBoundary Value Problems1687-27621687-27702006-02-01200610.1155/BVP/2006/37524A modified quasi-boundary value method for a class of abstract parabolic ill-posed problemsS. DjezzarM. DencheWe study a final value problem for first-order abstract differential equation with positive self-adjoint unbounded operator coefficient. This problem is ill-posed. Perturbing the final condition, we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions converge if and only if the original problem has a classical solution. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.http://dx.doi.org/10.1155/BVP/2006/37524
collection DOAJ
language English
format Article
sources DOAJ
author S. Djezzar
M. Denche
spellingShingle S. Djezzar
M. Denche
A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems
Boundary Value Problems
author_facet S. Djezzar
M. Denche
author_sort S. Djezzar
title A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems
title_short A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems
title_full A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems
title_fullStr A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems
title_full_unstemmed A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems
title_sort modified quasi-boundary value method for a class of abstract parabolic ill-posed problems
publisher SpringerOpen
series Boundary Value Problems
issn 1687-2762
1687-2770
publishDate 2006-02-01
description We study a final value problem for first-order abstract differential equation with positive self-adjoint unbounded operator coefficient. This problem is ill-posed. Perturbing the final condition, we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions converge if and only if the original problem has a classical solution. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.
url http://dx.doi.org/10.1155/BVP/2006/37524
work_keys_str_mv AT sdjezzar amodifiedquasiboundaryvaluemethodforaclassofabstractparabolicillposedproblems
AT mdenche amodifiedquasiboundaryvaluemethodforaclassofabstractparabolicillposedproblems
AT sdjezzar modifiedquasiboundaryvaluemethodforaclassofabstractparabolicillposedproblems
AT mdenche modifiedquasiboundaryvaluemethodforaclassofabstractparabolicillposedproblems
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