Abstract
We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions n \geq 2. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional conditions. A uniqueness result is derived as an immediate consequence of the stability result. Our approach relies on second-order linearization and multivariate finite differences, as well as the stability of the light-ray transform.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1937-1956 |
| Number of pages | 20 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 84 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2024 |
Bibliographical note
Publisher Copyright:© 2024 Society for Industrial and Applied Mathematics Publications. All rights reserved.
Keywords
- inverse problems
- logarithmic stability
- nonlinear Boltzmann equation
- time-dependent collision kernel