Determining a fractional Helmholtz equation with unknown source and scattering potential

Xinlin Cao, Hongyu LIU

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We are concerned with an inverse problem associated with a fractional Helmholtz equation that arises from the study of viscoacoustics in geophysics and thermoviscous modelling of lossy media. We are particularly interested in the case that both the medium parameter and the internal source of the wave equation are unknown. Moreover, we consider a general class of source functions which can be frequency-dependent. We establish several general uniqueness results in simultaneously recovering both the medium parameter and the internal source by the corresponding exterior measurements. In sharp contrast, these unique determination results are unknown in the local case, which would be of significant importance in thermo-and photo-acoustic tomography.

Original languageEnglish
Pages (from-to)1861-1876
Number of pages16
JournalCommunications in Mathematical Sciences
Volume17
Issue number7
DOIs
Publication statusPublished - 2019

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Compact embedding theorem
  • Fractional helmholtz equation
  • Low-frequency asymptotics
  • Runge approximation property
  • Simultaneous recovery
  • Strong uniqueness property

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