Abstract
We consider an inverse problem for the Boltzmann equation with nonlinear collision operator in dimensions n ≥ 2. We show that the kinetic collision kernel can be uniquely determined from the incoming-to-outgoing mappings on the boundary of the domain provided that the kernel satisfies a monotonicity condition. Furthermore, a reconstruction formula is also derived. The key methodology is based on the higher-order linearization scheme to reduce a nonlinear equation into simpler linear equations by introducing multiple small parameters into the original equation.
Original language | English (US) |
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Pages (from-to) | 1049-1069 |
Number of pages | 21 |
Journal | SIAM Journal on Mathematical Analysis |
Volume | 53 |
Issue number | 1 |
DOIs | |
State | Published - 2021 |
Bibliographical note
Publisher Copyright:© 2021 Society for Industrial and Applied Mathematics.
Keywords
- Boltzmann equation
- Collision operator
- Inverse problems
- Nonlinearity