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

2018/02/19 by Hyung Ju Hwang, Hwang, Hyung Ju, Juhi Jang +3
Physics and Astronomy · Mathematics · #Advanced Thermodynamics and Statistical Mechanics #Gas Dynamics and Kinetic Theory #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1802.06937

Abstract

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

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