The nonlinear diffusion limit for generalized Carleman models: the initial-boundary value problem
Year: 2007
Type: article
Abstract: Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases, (see Carleman 1957 Problèmes Mathématiques Dans la Théorie Cinétique des Gaz (Uppsala: Almqvist-Wiksells)), set in some bounded interval with boundary conditions prescribing the density of particles entering the interval. Under the usual parabolic scaling, a nonlinear diffusion limit is established for this problem. In fact, the techniques presented here allow treatment generalizations of the Carleman system where the collision frequency is proportional to the αth power of the macroscopic density, with α ∊ [−1, 1].
Source: Nonlinearity
Authors: François Golse, Francesco Salvarani
Institutions: Laboratoire Jacques-Louis Lions, University of Pavia
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2022981864