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.

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

E Bonetti;P Colli;
2017

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.
2017
Istituto di Matematica Applicata e Tecnologie Informatiche - IMATI -
Diffusion of species
forward-backward parabolic equation
hysteresis
initial-boundary value problem
non-smooth regularization
well-posedness
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Descrizione: A non-smooth regularization of a forward-backward parabolic equation
Tipologia: Versione Editoriale (PDF)
Dimensione 317.92 kB
Formato Adobe PDF
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14243/330797
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