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arXiv · 1508.03225

A non-smooth regularization of a forward-backward parabolic equation

Elena Bonetti·Pierluigi Colli·Giuseppe Tomassetti
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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.

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Elena Bonetti, Pierluigi Colli, Giuseppe Tomassetti. 2015-08-13. A non-smooth regularization of a forward-backward parabolic equation. https://arxiv.org/abs/1508.03225

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