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Asymptotic behavior of Nernst-Planck equation

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Date
2019
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
10-2019
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-02310654
Dewey
Analyse
Sujet
Nernst-Planck equation; large time asymptotic; free energy; Fisher information
URI
https://basepub.dauphine.fr/handle/123456789/20334
Collections
  • CEREMADE : Publications
Metadata
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Author
Li, Xingyu
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
23
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.

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