An inverse problem of finding a time-dependent coefficient in a fractional diffusion equation
D. K. Durdiev, DILSHOD DURDIEV
Abstract
This article is concerned with the study of unique solvability of an inverse coefficient problem of determining the coefficient at the lower term of a fractional diffusion equation. The direct problem is the initial-boundary problem for this equation with usual initial and homogeneous Dirichlet conditions. To determine the unknown coefficient, an overdetermination condition is given as the Neumann condition at the left end of the spatial interval. The theorems of existence and uniqueness of inverse problem solution are obtained. Furthermore, we propose a numerical algorithm based on a finite-difference scheme to accurately compute the inverse problem of simultaneously determining a time-dependent coefficient in a fractional diffusion equation, together with its solution. A test example using the developed numerical algorithm is presented herein.