Traveling phase interfaces in viscous forward-backward diffusion equations
Analysis of PDEs
2023-11-21 v1
Abstract
The viscous regularization of an ill-posed diffusion equation with bistable nonlinearity predicts a hysteretic behavior of dynamical phase transitions but a complete mathematical \mbox{understanding} of the intricate multiscale evolution is still missing. We shed light on the fine structure of \mbox{propagating} phase boundaries by carefully examining traveling wave solutions in a special case. Assuming a trilinear constitutive relation we characterize all waves that possess a monotone \mbox{profile} and connect the two phases by a single interface of positive width. We further study the two sharp-interface regimes related to either vanishing viscosity or the bilinear limit.
Cite
@article{arxiv.2311.11573,
title = {Traveling phase interfaces in viscous forward-backward diffusion equations},
author = {Carina Geldhauser and Michael Herrmann and Dirk Janßen},
journal= {arXiv preprint arXiv:2311.11573},
year = {2023}
}