ON THE STRUCTURE OF THE SINGULAR SET FOR THE KINETIC FOKKER-PLANCK EQUATIONS IN DOMAINS WITH BOUNDARIES
SCIE
SCOPUS
- Title
- ON THE STRUCTURE OF THE SINGULAR SET FOR THE KINETIC FOKKER-PLANCK EQUATIONS IN DOMAINS WITH BOUNDARIES
- Authors
- Hwang, Hyung Ju; Jang, Juhi; Velazquez, Juan J. L.
- Date Issued
- 2019-03
- Publisher
- BROWN UNIV
- 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 (Nonuniqueness for the kinetic-Fokker-Planck equation with inelastic boundary conditions) to prove rigorously nonuniqueness of solutions for the kinetic Fokker-Planck equation with inelastic boundary conditions.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/100164
- DOI
- 10.1090/qam/1507
- ISSN
- 0033-569X
- Article Type
- Article
- Citation
- QUARTERLY OF APPLIED MATHEMATICS, vol. 77, no. 1, page. 19 - 70, 2019-03
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