Hysteresis and phase transitions in a lattice regularization of an ill-posed forward-backward diffusion equation
Analysis of PDEs
2020-03-13 v2 Dynamical Systems
Abstract
We consider a lattice regularization for an ill-posed diffusion equation with trilinear constitutive law and study the dynamics of phase interfaces in the parabolic scaling limit. Our main result guarantees for a certain class of single-interface initial data that the lattice solutions satisfy asymptotically a free boundary problem with hysteretic Stefan condition. The key challenge in the proof is to control the microscopic fluctuations that are inevitably produced by the backward diffusion when a particle passes the spinodal region.
Keywords
Cite
@article{arxiv.1610.05447,
title = {Hysteresis and phase transitions in a lattice regularization of an ill-posed forward-backward diffusion equation},
author = {Michael Helmers and Michael Herrmann},
journal= {arXiv preprint arXiv:1610.05447},
year = {2020}
}
Comments
37 pages, several figures; revised version with enhanced introduction and several minor improvements