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.

Bonetti, E., Colli, P., & Tomassetti, G. (2017). A non-smooth regularization of a forward-backward parabolic equation. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 27(4), 641-661 [10.1142/S0218202517500129].

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

Tomassetti G.
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.
Bonetti, E., Colli, P., & Tomassetti, G. (2017). A non-smooth regularization of a forward-backward parabolic equation. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 27(4), 641-661 [10.1142/S0218202517500129].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/365278
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