Existence and uniqueness of a global weak solution of a Darcy‐Nernst‐Planck‐Poisson system

Kurzfassung/Abstract

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)