Recovering the potential term in a fractional diffusion equation

Zhidong Zhang, Zhi Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)

Abstract

In this article, we consider an inverse problem of recovering the potential term in a 1D time-fractional diffusion equation from the overdetermined final time data. We introduce a reconstruction operator and show its contractivity and monotonicity, which give the unique determination and an efficient algorithm. Further, for noisy data, we propose a regularized iterative algorithm based on mollification and derive error estimates for the approximation. Extensive numerical experiments for both smooth and nonsmooth potential data are provided to illustrate the efficiency and stability of the algorithm, and to verify the convergence theory.

Original languageEnglish
Pages (from-to)579-600
Number of pages22
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume82
Issue number3
DOIs
Publication statusPublished - 27 Feb 2017
Externally publishedYes

Keywords

  • Contraction
  • Fractional diffusion
  • Inverse potential problem
  • Iterative algorithm
  • Monotonicity
  • Regularization

ASJC Scopus subject areas

  • Applied Mathematics

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