Regularization of sideways problem for a time fractional diffusion equation with nonlinear source

2019/10/08 by Ngoc, Tran Bao, Tuan, Nguyen Huy, Kirane, Mokhtar
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.03228

Abstract

In this paper, we consider an inverse problem for a time-fractional diffusion equation with a nonlinear source. We prove that the considered problem is ill-posed, i.e. the solution does not depend continuously on the data. The problem is ill-posed in the sense of Hadamard. Under some weak \colorblack a priori assumptions on the sought solution, we propose a new regularization method for stabili\colorblackzing the ill-posed problem. We also provide a numerical example to illustrate our results.

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