Nonuniqueness for the Kinetic Fokker-Planck Equation with Inelastic Boundary Conditions
SCIE
SCOPUS
- Title
- Nonuniqueness for the Kinetic Fokker-Planck Equation with Inelastic Boundary Conditions
- Authors
- Hwang, Hyung Ju; Jang, Juhi; Velazquez, Juan J. L.
- Date Issued
- 2019-03
- Publisher
- SPRINGER
- 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
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/100180
- DOI
- 10.1007/s00205-018-1299-0
- ISSN
- 0003-9527
- Article Type
- Article
- Citation
- ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, vol. 231, no. 3, page. 1309 - 1400, 2019-03
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