Reconstruction of a space-time dependent source in subdiffusion models via a perturbation approach

Bangti Jin, Yavar Kian, Zhi Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)

Abstract

In this article we study two inverse problems of recovering a space-time-dependent source component from the lateral boundary observation in a subdiffusion model. The mathematical model involves a Djrbashian-Caputo fractional derivative of order α ∊ (0, 1) in time, and a second-order elliptic operator with time-dependent coefficients. We establish a well-posedness and a conditional stability result for the inverse problems using a novel perturbation argument and refined regularity estimates of the associated direct problem. Further, we present a numerical algorithm for efficiently and accurately reconstructing the source component, and we provide several two-dimensional numerical results showing the feasibility of the recovery.

Original languageEnglish
Pages (from-to)4445-4473
Number of pages29
JournalSIAM Journal on Mathematical Analysis
Volume53
Issue number4
DOIs
Publication statusPublished - Jul 2021

Keywords

  • Conditional stability
  • Inverse source problem
  • Reconstruction
  • Subdiffusion
  • Time-dependent coefficient

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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