A non-smooth regularization of a forward-backward parabolic equation
Abstract
In this paper we introduce a model describing diffusion of species by a suitable regularization of a "forward-backward" parabolic equation. In particular, we prove existence and uniqueness of solutions, as well as continuous dependence on data, for a system of partial differential equations and inclusion, which may be interpreted, e.g., as evolving equation for physical quantities such as concentration and chemical potential. The model deals with a constant mobility and it is recovered from a possibly non-convex free-energy density. In particular, we render a general viscous regularization via a maximal monotone graph acting on the time derivative of the concentration and presenting a strong coerciveness property.
Cite
@article{arxiv.1508.03225,
title = {A non-smooth regularization of a forward-backward parabolic equation},
author = {Elena Bonetti and Pierluigi Colli and Giuseppe Tomassetti},
journal= {arXiv preprint arXiv:1508.03225},
year = {2015}
}
Comments
Key words: diffusion of species, forward-backward parabolic equation, non-smooth regularization, initial-boundary value problem, well-posedness, hysteresis