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

Khelili Besma 1 , Boussetila Nadjib 2  and Rebbani Faouzia 3
  • 1 20 Aout 55 Skikda University, Faculty of Science, Skikda, Algeria
  • 2 Department of Mathematics, FMISM, 8 Mai 1945 Guelma University, P.O.Box 401, Guelma, Algeria
  • 3 Applied Mathematics Laboratory, University Badji Mokhtar Annaba, P.O.Box 12, Annaba, Algeria

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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