Degenerate drift-diffusion systems for memristors
Analysis of PDEs
2023-11-29 v1
Abstract
A system of degenerate drift-diffusion equations for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a three-dimensional bounded domain with mixed Dirichlet-Neumann boundary conditions. The equations model the dynamics of the charge carriers in a memristor device in the high-density regime. Memristors can be seen as nonlinear resistors with memory, mimicking the conductance response of biological synapses. The global existence of weak solutions and the weak-strong uniqueness property is proved. Thanks to the degenerate diffusion, better regularity results compared to linear diffusion can be shown, in particular the boundedness of the solutions.
Cite
@article{arxiv.2311.16591,
title = {Degenerate drift-diffusion systems for memristors},
author = {Ansgar Jüngel and Martin Vetter},
journal= {arXiv preprint arXiv:2311.16591},
year = {2023}
}