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Regularization and error estimate for an initial inverse nonlocal diffusion problem
Journal article   Peer reviewed

Regularization and error estimate for an initial inverse nonlocal diffusion problem

Nguyen Huy Tuan, Bui Le Trong Thanh, Mokhtar Kirane and Phan Thi Khanh Van
Computers & mathematics with applications (1987), Vol.79(12), pp.3331-3352
15/06/2020
DOI: https://doi.org/10.1016/j.camwa.2020.01.029

Abstract

Fourier truncation method Ill-posed problem Inverse problem Nonlocal diffusion Population density Quasi-reversibility method
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.

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