Regularization and error estimate for an initial inverse nonlocal diffusion problem

Nguyen Huy Tuan, Bui Le Trong Thanh, Mokhtar Kirane, Phan Thi Khanh Van

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageBritish English
Pages (from-to)3331-3352
Number of pages22
JournalComputers and Mathematics with Applications
Issue number12
StatePublished - 15 Jun 2020


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


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