A modified quasi-boundary value method for an abstract ill-posed biparabolic problem

In this paper, we are concerned with the problem of approximating a solution of an ill-posed biparabolic problem in the abstract setting. In order to overcome the instability of the original problem, we propose a modified quasi-boundary value method to construct approximate stable solutions for the...

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Bibliographic Details
Published in:Open mathematics (Warsaw, Poland) Vol. 15; no. 1; pp. 1649 - 1666
Main Authors: Besma, Khelili, Nadjib, Boussetila, Faouzia, Rebbani
Format: Journal Article
Language:English
Published: Warsaw De Gruyter Open 29.12.2017
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
De Gruyter
Subjects:
47A52
65J22
Approximation
Biparabolic problem
Boundary value problems
Convergence
Exact solutions
Ill posed problems
Regularization
ISSN:2391-5455, 2391-5455
Online Access:Get full text
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Summary:In this paper, we are concerned with the problem of approximating a solution of an ill-posed biparabolic problem in the abstract setting. In order to overcome the instability of the original problem, we propose a modified quasi-boundary value method to construct approximate stable solutions for the original ill-posed boundary value problem. Finally, some other convergence results including some explicit convergence rates are also established under a priori bound assumptions on the exact solution. Moreover, numerical tests are presented to illustrate the accuracy and efficiency of this method.
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ISSN:2391-5455
2391-5455
DOI:10.1515/math-2017-0140