Parameter reconstruction for general transport equation

Ru Yu Lai, Qin Li

Research output: Contribution to journalArticlepeer-review


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
Issue number3
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. 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 ( \ddagger Department of Mathematics, University of Wisconsin--Madison, Madison, WI 53706 (qinli@math.

Publisher Copyright:
© 2020 Society for Industrial and Applied Mathematics.


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


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