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.
@article{bwmeta1.element.doi-10_1515_math-2017-0140,
author = {Khelili Besma and Boussetila Nadjib and Rebbani Faouzia},
title = {A modified quasi-boundary value method for an abstract ill-posed biparabolic problem},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {1649-1666},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0140}
}
Khelili Besma; Boussetila Nadjib; Rebbani Faouzia. A modified quasi-boundary value method for an abstract ill-posed biparabolic problem. Open Mathematics, Tome 15 (2017) pp. 1649-1666. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0140/