Identifying temperature distribution and source term for generalized diffusion equation with arbitrary memory kernel

Abstract

A diffusion equation involving integral convolution in time variable with arbitrary kernel and nonlocal boundary conditions is considered. The existence and uniqueness results for two inverse problems of determining source terms (space‐ and time‐dependent sources) along with diffusion concentration from appropriate over‐specified conditions are presented. A bi‐orthogonal system of functions is used to have series representation of the solutions of the inverse problems. Several special cases such as standard diffusion, multi‐term diffusion, and tempered diffusion equations are discussed, and some examples are provided.