Reconstruction of the collision kernel in the nonlinear Boltzmann equation

2020/03/21 by Lai, Ru-Yu, Uhlmann, Gunther, Yang, Yang · 4 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.09549

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.

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