Premium
Existence and uniqueness of a global weak solution of a Darcy‐Nernst‐Planck‐Poisson system
Author(s) -
Herz Matthias,
Ray Nadja,
Knabner Peter
Publication year - 2012
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201210013
Subject(s) - uniqueness , nernst equation , planck , electrolyte , poisson distribution , nonlinear system , mathematics , mathematical analysis , physics , quantum mechanics , statistics , electrode
This paper deals with the analytical investigations of a nonstationary Darcy‐Nernst‐Planck‐Poisson‐type system which is a mathematical model describing electrolyte solutions. For this nonlinear fully coupled system of partial differential equations we proof existence and uniqueness of global weak solutions. Furthermore, we establish physical properties for the number densities such as nonnegativity and boundedness in L ∞ ((0, T ) × Ω) (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)