Abstract
The mathematical model of the transport and diffusion of ions in biological channels is considered. It is described by the three-dimensional nonlinear evolution classical Poisson–Nernst–Planck (cPNP) system of partial differential equations with nonlinear coupled boundary conditions. In particular the Chang–Jaffé (CJ) conditions are given on the input and output of a channel. The Robin boundary conditions on a potential are taken. Theorems on the existence, uniqueness and nonnegativity of local weak solutions, in the suitable Sobolev spaces, are proved. The main tool used in the proof of the existence result is the Schauder–Tychonoff fixed point theorem.
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