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NUMBER  
AUTHOR Jang, Juhi
TITLE Nonuniqueness for the Kinetic Fokker-Planck Equation with Inelastic Boundary Conditions
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FILE  
JOURNAL ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2019
ABSTRACT We describe the structure of solutions of the kinetic Fokker-Planck equations in domains with boundaries near the singular set in one-space dimension. We study in particular the behaviour of the solutions of this equation for inelastic boundary conditions which are characterized by means of a coefficient r describing the amount of energy lost in the collisions of the particles with the boundaries of the domain. A peculiar feature of this problem is the onset of a critical exponent r(c) which follows from the analysis of McKean (J Math Kyoto Univ 2:227-235 1963) of the properties of the stochastic process associated to the Fokker-Planck equation under consideration. In this paper, we prove rigorously that the solutions of the considered problem are nonunique if r
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