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- Title
The linearized Poisson–Nernst–Planck system as heat flow on the interval under non‐local boundary conditions.
- Authors
Wolansky, Gershon
- Abstract
The linearized 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 resolvent operator and recover the heat kernel by applying the inverse Laplace transform.
- Subjects
HEATING; THERMAL expansion; RESOLVENTS (Mathematics); HEAT equation; EIGENVALUES
- Publication
Mathematical Methods in the Applied Sciences, 2024, Vol 47, Issue 6, p4094
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9805