Regularization and error estimate for an initial inverse nonlocal diffusion problem

Abstract

We study the backward problem of determining the initial condition for a system of parabolic diffusion equations, which is severely ill-posed in the sense of Hadamard. To stabilize the solution, we develop the quasi-reversibility (QR) and Fourier truncation methods to construct the regularized solutions. We also investigate the error estimates and convergence rates between the regularized solutions and the true solution in L2− and H1−norm. A numerical scheme is presented.