An inverse problem for a two‐dimensional diffusion equation with arbitrary memory kernel

Abstract

An inverse source problem (ISP) of recovering space‐dependent source term along with diffusion concentration for a two‐dimensional diffusion equation involving integral convolution of arbitrary memory kernel in time is considered. The unique existence of the solution is proved using a bi‐orthogonal system of functions obtained from the associated non‐self‐adjoint spectral problem and its adjoint problem which form Riesz basis in . In addition, some particular cases of ISP are described as special cases of our results.