Recovery of the solute concentration and dispersion flux in an inhomogeneous time fractional diffusion equation

摘要

In this paper, we consider recovery of solute concentration and dispersion flux in an inhomogeneous time fractional diffusion equation. We prove that the considered problem is ill-posed, i.e. the solution does not depend continuously on the data. In order to obtain a regularized solution, we propose a truncation regularization method. The convergence estimates are established under some priori bound assumptions for the exact solution. We present three numerical examples to show efficiency of the method.