Parameter reconstruction for general transport equation

Ru Yu Lai, Qin Li

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the inverse problem for the general transport equation with external field, source term, and absorption coefficient. We show that the source and the absorption coefficients can be uniquely reconstructed from the boundary measurement in a Lipschitz stable manner. Specifically, the uniqueness and stability are obtained by using the Carleman estimate, in which a special weight function is designed to pick up information on the desired parameter.

Original languageEnglish (US)
Pages (from-to)2734-2758
Number of pages25
JournalSIAM Journal on Mathematical Analysis
Volume52
Issue number3
DOIs
StatePublished - 2020

Bibliographical note

Funding Information:
\ast Received by the editors June 3, 2019; accepted for publication (in revised form) March 5, 2020; published electronically June 8, 2020. https://doi.org/10.1137/19M1265739 Funding: The work of the first author was partially supported by National Science Foundation grant DMS-1714490. The work of the second author was partially supported by National Science Foundation grants DMS-1619778, DMS-1750488. \dagger School of Mathematics, University of Minnesota, Minneapolis, MN 55455 (rylai@umn.edu). \ddagger Department of Mathematics, University of Wisconsin--Madison, Madison, WI 53706 (qinli@math. wisc.edu).

Keywords

  • Carleman estimate
  • General transport equation
  • Inverse problem
  • Stability estimate

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