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 language | English (US) |
|---|---|
| Pages (from-to) | 2734-2758 |
| Number of pages | 25 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 52 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2020 |
Bibliographical note
Publisher Copyright:© 2020 Society for Industrial and Applied Mathematics.
Keywords
- Carleman estimate
- General transport equation
- Inverse problem
- Stability estimate
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