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arXiv · 1802.06937

On the structure of the singular set for the kinetic Fokker-Planck equations in domains with boundaries

Hyung Ju Hwang·Juhi Jang·Juan J. L. Velázquez
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Abstract

In this paper we compute asymptotics of solutions of the kinetic Fokker-Planck equation with inelastic boundary conditions which indicate that the solutions are nonunique if $r < r_c$. The nonuniqueness is due to the fact that different solutions can interact in a different manner with a Dirac mass which appears at the singular point $(x,v)=(0,0)$. In particular, this nonuniqueness explains the different behaviours found in the physics literature for numerical simulations of the stochastic differential equation associated to the kinetic Fokker-Planck equation. The asymptotics obtained in this paper will be used in a companion paper [34] to prove rigorously nonuniqueness of solutions for the kinetic Fokker-Planck equation with inelastic boundary conditions.

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Hyung Ju Hwang, Juhi Jang, Juan J. L. Velázquez. 2018-02-20. On the structure of the singular set for the kinetic Fokker-Planck equations in domains with boundaries. https://arxiv.org/abs/1802.06937

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