학술논문
Existence and uniqueness theorems for the Boltzmann equation.
Document Type
Proceedings Paper
Author
Palczewski, A. (PL-WASW) AMS Author Profile
Source
Subject
35 Partial differential equations -- 35Q Equations of mathematical physics and other areas of application
35Q20Boltzmann equations
45Integral equations -- 45K Integro-partial differential equations
45K05Integro-partial differential equations
82Statistical mechanics, structure of matter -- 82A Statistical physics, structure of matter
82A40Kinetic theory of gases
35Q20
45
45K05
82
82A40
Language
English
Abstract
This article is a review of results and proofs concerning existence and uniqueness of solutions of the Boltzmann equation which are due to Carleman, Maslova-Chubenko, Gluck, Morgenstern, Povzner, Arkeryd, Elmroth in the space homogenous case, and to Grad, Kaniel-Shinbrot (as for local solutions) and to Ukai, Imai-Nishida, Illner-Shinbrot (as for global solutions) in the space inhomogenous case. The list of references contains 32 items, among which the most recent ones date back to 1986.