Abstract
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.
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