Determination of Robin coefficient in a fractional diffusion problem

Abstract

This paper investigates a nonlinear inverse problem associated with a fractional diffusion equation for identifying a Robin coefficient in the boundary conditions from a boundary measurement. The existence and uniqueness of a weak solution for the corresponding direct problem is provided. We formulate the inverse problem into a regularized variational problem and deduce the gradient of the regularization functional based on an adjoint problem. Then the standard conjugate gradient method is employed to solve the variational problem. The numerical results for three examples are presented to illustrate the efficiency of the proposed algorithm.