Inverse source problem with a posteriori boundary measurement for fractional diffusion equations

Abstract

In this article, we study inverse source problems for time‐fractional diffusion equations from a posteriori boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class of space‐ or time‐dependent source terms. We prove also the unique determination of a general class of space–time‐dependent separated variables source terms from such measurement. Our approach is based on the study of singularities of the Laplace transform in time of boundary traces of solutions of time‐fractional diffusion equations.