The nonlinear diffusion limit for generalized Carleman models: the initial-boundary value problem

Details The nonlinear diffusion limit for generalized Carleman models: the initial-boundary value problem The nonlinear diffusion limit for generalized Carleman models: the initial-boundary value problem

2007-02-23

arxiv.org/abs/math/0702705v1

Mathematics

Analysis of PDEs

Scientific paper

Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases 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 treating generalizations of the Carleman system where the collision frequency is proportional to some power of the macroscopic density, with exponent in [-1,1].

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