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 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Warsaw
De Gruyter Open
29.12.2017
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services De Gruyter |
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| ISSN: | 2391-5455, 2391-5455 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Faouzia, Rebbani Besma, Khelili Nadjib, Boussetila |
| Author_xml | – sequence: 1 givenname: Khelili surname: Besma fullname: Besma, Khelili email: kh86basma@yahoo.com organization: 20 Aout 55 Skikda University, Faculty of Science, Skikda, Algeria – sequence: 2 givenname: Boussetila surname: Nadjib fullname: Nadjib, Boussetila email: n.boussetila@gmail.com organization: Department of Mathematics, FMISM, 8 Mai 1945 Guelma University, P.O.Box 401, Guelma, 24000, Algeria – sequence: 3 givenname: Rebbani surname: Faouzia fullname: Faouzia, Rebbani email: f.rebbani@epst-annaba.dz organization: Applied Mathematics Laboratory, University Badji Mokhtar Annaba, P.O.Box 12, Annaba, 23000, Algeria |
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| Cites_doi | 10.1007/s10559-008-9036-6 10.1080/17415977.2011.552111 10.1016/0022-247X(74)90008-0 10.1007/BF01071016 10.1016/j.physleta.2013.07.009 10.1515/GMJ.2007.627 10.1515/jiip.2010.030 10.1515/jiip.2010.028 10.1007/s11075-011-9487-0 10.1142/S0218202598000093 10.1093/imamat/hxh112 10.1080/00207160.2012.693174 10.1016/0041-5553(85)90079-5 10.1137/090780225 10.1093/imamat/hxp026 10.1007/BF00971100 10.1016/j.ijengsci.2017.06.006 10.1016/j.jmaa.2008.04.064 10.1007/s00211-010-0318-3 |
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| SubjectTerms | 47A52 65J22 Approximation Biparabolic problem Boundary value problems Convergence Exact solutions Ill posed problems Regularization |
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| Title | A modified quasi-boundary value method for an abstract ill-posed biparabolic problem |
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