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Large Time Asymptotic of Nonlinear Drift-Diffusion Systems with Poisson Coupling

Biler, Piotr; Dolbeault, Jean; Markowich, Peter (2001), Large Time Asymptotic of Nonlinear Drift-Diffusion Systems with Poisson Coupling, Transport Theory and Statistical Physics, 30, 4-6, p. 521-536. http://dx.doi.org/10.1081/TT-100105936

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Type
Article accepté pour publication ou publié
Date
2001
Journal name
Transport Theory and Statistical Physics
Volume
30
Number
4-6
Publisher
Taylor & Francis
Pages
521-536
Publication identifier
Metadata
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Author(s)
Biler, Piotr
Dolbeault, Jean cc
Markowich, Peter
Abstract (EN)
We study the asymptotic behavior as t→ +∞ 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 spatio-temporal 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.
Subjects / Keywords
Nonlinear drift-diffusion systems; Asymptotic behavior of solutions; Logarithmic sobolev inequalities; Fast diffusion; Porous media