Regularization method for an ill-posed Cauchy problem for elliptic equations

Benrabah, Abderafik; Boussetila, Nadjib; Rebbani, Faouzia

doi:10.1515/jiip-2015-0075

Cited by 4 publications

(1 citation statement)

References 36 publications

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“…Khelili et al considered a modified QBVM for an abstract ill‐posed biparabolic problem. Zouyed and Rebbani considered the ultraparabolic ill‐posed problem, and Benrabah et al considered a QBVM combined with a qausi‐reversibility method for an ill posed elliptic problem.…”

Section: Introductionmentioning

confidence: 99%

Modified auxiliary boundary conditions method for an ill‐posed problem for the homogeneous biharmonic equation

Benrabah

Boussetila

Rebbani³

2019

Math Methods in App Sciences

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In this paper, we are interested in the inverse problem for the biharmonic equation posed on a rectangle, which is of great importance in many areas of industry and engineering. We show that the problem under consideration is ill-posed; therefore, to solve it, we opted for a regularization method via modified auxiliary boundary conditions. The numerical implementation is based on the application of the semidiscrete finite difference method for a sequence of well-posed direct problems depending on a small parameter of regularization. Numerical results are performed for a rectangle domain showing the effectiveness of the proposed method. KEYWORDS auxiliary boundary conditions, biharmonic equation, convergence estimate, ill-posed problems, plates, regularization MSC CLASSIFICATION 35J40; 31B30; 35B45; 74K20; 47A52 Abbreviations: BHP, biharmonic problem; MABCM, modified auxiliary boundary conditions method; QBVM, quasi-boundary value method. wileyonlinelibrary.com/journal/mma

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Section: Introductionmentioning

confidence: 99%