Determining the collision kernel in the Boltzmann equation near the equilibrium
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- by Li Li and Zhimeng Ouyang
- Proc. Amer. Math. Soc. 151 (2023), 4855-4865
- DOI: https://doi.org/10.1090/proc/16522
- Published electronically: August 18, 2023
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Abstract:
We consider an inverse problem for the nonlinear Boltzmann equation near the equilibrium. Our goal is to determine the collision kernel in the Boltzmann equation from the knowledge of the Albedo operator. Our approach relies on a linearization technique as well as the injectivity of the Gauss-Weierstrass transform.References
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Bibliographic Information
- Li Li
- Affiliation: Institute for Pure and Applied Mathematics, University of California, Los Angeles, California 90095
- ORCID: 0000-0002-1933-6669
- Email: lili@ipam.ucla.edu
- Zhimeng Ouyang
- Affiliation: Institute for Pure and Applied Mathematics, University of California, Los Angeles, California 90095
- MR Author ID: 1375691
- ORCID: 0000-0002-5753-0278
- Email: zouyang@ipam.ucla.edu
- Received by editor(s): September 5, 2022
- Received by editor(s) in revised form: April 23, 2023
- Published electronically: August 18, 2023
- Additional Notes: The authors were partly supported by the Simons Foundation.
- Communicated by: Benoit Pausader
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 4855-4865
- MSC (2020): Primary 35R30; Secondary 35Q20
- DOI: https://doi.org/10.1090/proc/16522
- MathSciNet review: 4634888