On the convergence rate of an improved quasi-reversibility method for an inverse source problem of a nonlinear parabolic equation with nonlocal diffusion coefficient

This paper investigates the identification of the space-dependent source term in a nonlinear parabolic equation with nonlocal diffusion coefficient, which means that the diffusion process modelled by the above nonlinear parabolic equation depends on the population itself in biology and ecology fields. The nonlinear expansion of the solution to direct problem is established firstly, in terms of which an improved quasi-reversibility method for the inverse problem is proposed. Then to overcome the difficulty of nonlinear and nonlocal of the problem, the reasonable convergence rate of the regularizing solution under the bounded conditions is derived rigorously, with the choice strategy for the regularizing parameter. (C) 2021 Elsevier Ltd. All rights reserved.