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Seminario di Equazioni Differenziali e Applicazioni: “Regularity of the Boltzmann equation in bounded domains”

Mercoledì 28 Febbraio 2018, ore 12:00 - Aula 2BC30 - Daniela Tonon

ARGOMENTI: Seminari

Mercoledì 28 Febbraio 2018 alle ore 12:00 in Aula 2BC30, Daniela Tonon (Ceremade - Université Paris Dauphine, Parigi) terrà un seminario dal titolo “Regularity of the Boltzmann equation in bounded domains”.

Abstract
The Boltzmann equation models the dynamic of non-equilibrium rarefied gases. Despite extensive developments in the study of this equation, many basic questions regarding solutions in a physical bounded domain, such as their regularity, have remained largely open. This is partly due to the characteristic nature of boundary conditions in kinetic theory and to the non-local mixing of the collision operator. We introduce the problem considering several different boundary conditions and show some regularity result making the difference between convex and non convex domain. The solution is known to present a singular behavior on the grazing trajectories. In the case of a strictly convex domain, the singularities happen specifically on the (grazing) boundary and Sobolev regularity or weighted $C^1$ regularity of the solution can be proved. In the case of a non-convex domain, the singular trajectories cross the domain and the singularity propagates in the domain: in this case less regularity is expected.
This is a joint work with Yan Guo, Chanwoo Kim and Ariane Trescases.

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