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Asymptotic behavior of Nernst-Planck equation

Li, Xingyu (2019), Asymptotic behavior of Nernst-Planck equation. https://basepub.dauphine.fr/handle/123456789/20334

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02310654
Date
2019
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
23
Metadata
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Author(s)
Li, Xingyu
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
This paper is devoted to the Nernst-Planck system of equations with an external potential of confinement. The main result is concerned with the asymptotic behaviour of the solution of the Cauchy problem. We will prove that the optimal exponential rate of convergence of the solution to the unique stationary solution is determined by the spectral gap of the linearized problem around the minimizer of the free energy. The key issue is to consider an adapted notion of scalar product.
Subjects / Keywords
Nernst-Planck equation; large time asymptotic; free energy; Fisher information