The linearized Poisson-Nernst-Planck system as heat flow on the interval under non-local boundary conditions
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Publication:6364513
DOI10.1002/MMA.9805arXiv2104.01585OpenAlexW4389117019MaRDI QIDQ6364513
Publication date: 4 April 2021
Abstract: 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 reveals the eigenvalues and eigenstates of both the PNP equation and its adjoint. For this, we take advantage of the representation of the resulvent operator and recover the heat kernel by applying the inverse Laplace transform.
Full work available at URL: https://doi.org/10.1002/mma.9805
Fundamental solutions to PDEs (35A08) Transform methods (e.g., integral transforms) applied to PDEs (35A22)
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