Solvability and lyapunov stability of a two-component system of generalized poisson-nernst-planck equations

Abstract

A time-dependent Poisson-Nernst-Planck system of nonlinear partial differential equations of a mixed parabolic-elliptic type is considered. The generalized model is supplemented by a positivity and volume constraints, by dual entropy variables, and by nonlinear boundary conditions. The existence theorem supported by a priori estimates, the Lyapunov stability of the solution, and its uniqueness in a special case are proved.