A modified quasi-boundary value method for an abstract ill-posed biparabolic problem - Besma, Khelili; Nadjib, Boussetila; Faouzia, Rebbani (Open mathematics (Warsaw, Poland), 2017)
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.