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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Vydáno v:Open mathematics (Warsaw, Poland) Ročník 15; číslo 1; s. 1649 - 1666
Hlavní autoři: Besma, Khelili, Nadjib, Boussetila, Faouzia, Rebbani
Médium: Journal Article
Jazyk:angličtina
Vydáno: Warsaw De Gruyter Open 29.12.2017
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
De Gruyter
Témata:
47A52
65J22
Approximation
Biparabolic problem
Boundary value problems
Convergence
Exact solutions
Ill posed problems
Regularization
ISSN:2391-5455, 2391-5455
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:2391-5455
2391-5455
DOI:10.1515/math-2017-0140