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Taylor and Francis Group, Transport Theory and Statistical Physics, 4-6(30), p. 521-536, 2001

DOI: 10.1081/tt-100105936

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Large time asymptotics of nonlinear drift-diffusion systems with poisson coupling

Journal article published in 2001 by Piotr Biler, Jean Dolbeault ORCID, Peter A. Markowich
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This paper is available in a repository.

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Abstract

We study the asymptotic behavior as ... of a system of densities of charged particles satisfying nonlinear drift-diffusion equations coupled by a damped Poisson equation for the drift-potential. In plasma physics applications the damping is caused by a spatiotemporal rescaling of an "unconfined" problem, which introduces a harmonic external potential of confinement. We present formal calculations (valid for smooth solutions) which extend the results known in the linear diffusion case to nonlinear diffusion of e.g. Fermi-Dirac or fast diffusion/porous media type.