Regularization of a sideways problem for a time-fractional diffusion equation with nonlinear source

Tran Bao Ngoc, Nguyen Huy Tuan, Mokhtar Kirane

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper, we consider an inverse problem for a time-fractional diffusion equation with a nonlinear source. We prove that the considered problem is ill-posed, i.e., the solution does not depend continuously on the data. The problem is ill-posed in the sense of Hadamard. Under some weak a priori assumptions on the sought solution, we propose a new regularization method for stabilizing the ill-posed problem. We also provide a numerical example to illustrate our results.

Original languageBritish English
Pages (from-to)211-235
Number of pages25
JournalJournal of Inverse and Ill-Posed Problems
Volume28
Issue number2
DOIs
StatePublished - 1 Apr 2020

Keywords

  • Caputo's fractional derivatives
  • Fourier transform
  • Ill-posed
  • regularization method

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