On the structure of the singular set for the kinetic FokkerPlanck equations in domains with boundaries
Abstract
In this paper we compute asymptotics of solutions of the kinetic FokkerPlanck 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 FokkerPlanck equation. The asymptotics obtained in this paper will be used in a companion paper [34] to prove rigorously nonuniqueness of solutions for the kinetic FokkerPlanck equation with inelastic boundary conditions.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.06937
 Bibcode:
 2018arXiv180206937H
 Keywords:

 Mathematics  Analysis of PDEs;
 35Q84;
 35K65;
 35A20
 EPrint:
 41 pages, 3 figures, split off from arXiv:1509.03366