Entropy method for generalized Poisson–Nernst–Planck equations

Entropy method for generalized Poisson–Nernst–Planck equations Full article

Journal

Analysis and Mathematical Physics
ISSN: 1664-2368

Output data

Year: 2018, Volume: 8, Number: 4, Pages: 603-619 Pages count : 17 DOI: 10.1007/s13324-018-0257-1

Tags

Electrokinetics; Entropy variables; Fermi–Dirac statistics; Gibbs simplex; Gradient flow; Poisson–Nernst–Planck equations; Well-posedness analysis

Authors

González Granada José Rodrigo ¹ , Kovtunenko Victor A. ^2,3

Affiliations

1	Department of Mathematics, Universidad Tecnológica de Pereira
2	Institute for Mathematics and Scientific Computing, Karl-Franzens University of Graz
3	Lavrent’ev Institute of Hydrodynamics, Siberian Division of Russian Academy of Sciences

A proper mathematical model given by nonlinear Poisson–Nernst–Planck (PNP) equations which describe electrokinetics of charged species is considered. The model is generalized with entropy variables associating the pressure and quasi-Fermi electro-chemical potentials in order to adhere to the law of conservation of mass. Based on a variational principle for suitable free energy, the generalized PNP system is endowed with the structure of a gradient flow. The well-posedness theorems for the mixed formulation (using the entropy variables) of the gradient-flow problem are provided within the Gibbs simplex and supported by a-priori estimates of the solution.

González Granada J.R. , Kovtunenko V.A.
Entropy method for generalized Poisson–Nernst–Planck equations
Analysis and Mathematical Physics. 2018. V.8. N4. P.603-619. DOI: 10.1007/s13324-018-0257-1 WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000451394300008
Scopus:	2-s2.0-85057327850
Elibrary:	38199337
OpenAlex:	W2898886831

DB	Citing
Scopus	13
OpenAlex	14
Elibrary	13
Web of science	14