Inverse source problems in transport equations with external forces

Ru Yu Lai, Hanming Zhou

Research output: Contribution to journalArticlepeer-review

Abstract

This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular, for inverse problems, generic injectivity and a stability estimate of the source are derived. The analysis employs the Fredholm theorem and the Santalo's formula.

Original languageEnglish (US)
Pages (from-to)728-752
Number of pages25
JournalJournal of Differential Equations
Volume302
DOIs
StatePublished - Nov 25 2021

Bibliographical note

Funding Information:
RL was partially supported by NSF grant DMS-2006731 . HZ was partly supported by NSF grant DMS-2109116 .

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

  • Attenuated X-ray transform
  • Inverse source problems
  • Santalo's formula
  • Transport equations

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