The linearized of the Poisson-Nernst-Planck (PNP) equation under closed ends around a neutral state is studied. It is reduced to a damped heat equation under non-local boundary conditions, which leads to a stochastic interpretation of the linearized equation as a Brownian particle which jump and is reflected, at Poisson distributed time, to one of the end points of the channel, with a probability which is proportional to its distance from this end point. An explicit expansion of the heat kernel… Expand

Single charge densities and the potential are used to describe models of electrochemical systems. These quantities can be calculated by solving a system of time dependent nonlinear coupled partial… Expand

By the method of classical potential theory, we obtain the integral representation of the two-parameter operator semigroup that describes the inhomogeneous Feller process on a closed interval [ , ]… Expand

An exact analytical solution of the Poisson-Nernst-Planck equations in the linear regime is obtained, which is characterized by an inevitable coupling between the spatial and the temporal behavior.Expand

A physical process (a change of a certain physical system) is called stochastically determined if, knowing a state X 0 of the system at a certain moment of time t0 we also know the probability… Expand