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

Piotr Biler; Jean Dolbeault; Peter A. Markowich

doi:10.1081/TT-100105936

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

Piotr Biler, Jean Dolbeault, Peter A. Markowich^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

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.

Original language	English (US)
Pages (from-to)	521-536
Number of pages	16
Journal	Transport Theory and Statistical Physics
Volume	30
Issue number	4-6
DOIs	https://doi.org/10.1081/TT-100105936
State	Published - 2001
Externally published	Yes

Keywords

Asymptotic behavior of solutions
Fast diffusion
Logarithmic sobolev inequalities
Nonlinear drift-diffusion systems
Porous media

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Transportation
General Physics and Astronomy
Applied Mathematics

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10.1081/TT-100105936

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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.",

keywords = "Asymptotic behavior of solutions, Fast diffusion, Logarithmic sobolev inequalities, Nonlinear drift-diffusion systems, Porous media",

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AU - Biler, Piotr

AU - Dolbeault, Jean

AU - Markowich, Peter A.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - Asymptotic behavior of solutions

KW - Fast diffusion

KW - Logarithmic sobolev inequalities

KW - Nonlinear drift-diffusion systems

KW - Porous media

UR - http://www.scopus.com/inward/record.url?scp=0035636746&partnerID=8YFLogxK

U2 - 10.1081/TT-100105936

DO - 10.1081/TT-100105936

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AN - SCOPUS:0035636746

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VL - 30

SP - 521

EP - 536

JO - Transport Theory and Statistical Physics

JF - Transport Theory and Statistical Physics

IS - 4-6

ER -

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

Abstract

Keywords

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