Determination of an unknown source term temperature distribution for the sub-diffusion equation at the initial and final data

Abstract

We consider a class of problems modeling the process of determining the temperature and density of nonlocal sub-diffusion sources given by initial and finite temperature. Their mathematical statements involve inverse problems for the fractional-time heat equation in which, solving the equation, we have to find the an unknown right-hand side depending only on the space variable. The results on existence and uniqueness of solutions of these problems are presented.

Keywords

• Inverse problem
• involution
• nonlocal sub-diffusion equation
• fractional-time diffusion equation