Reconstruction of the collision kernel in the nonlinear Boltzmann equation

Ru Yu Lai, Gunther Uhlmann, Yang Yang

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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 languageEnglish (US)
Pages (from-to)1049-1069
Number of pages21
JournalSIAM Journal on Mathematical Analysis
Issue number1
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics.


  • Boltzmann equation
  • Collision operator
  • Inverse problems
  • Nonlinearity


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