Communications in Mathematical Physics

, Volume 308, Issue 3, pp 641–701 | Cite as

Formation and Propagation of Discontinuity for Boltzmann Equation in Non-Convex Domains



The formation and propagation of singularities for the Boltzmann equation in bounded domains has been an important question in numerical studies as well as in theoretical studies. In this paper, we consider the nonlinear Boltzmann solution near Maxwellians under in-flow, diffuse, or bounce-back boundary conditions. We demonstrate that discontinuity is created at the non-convex part of the grazing boundary, and then it propagates only along the forward characteristics inside the domain before it hits on the boundary again.


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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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