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.
Bibliographical noteFunding 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 (firstname.lastname@example.org). \ddagger Department of Mathematics, University of Wisconsin--Madison, Madison, WI 53706 (qinli@math. wisc.edu).
© 2020 Society for Industrial and Applied Mathematics.
- Carleman estimate
- General transport equation
- Inverse problem
- Stability estimate