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, G. Tomassetti. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - 27:4(2017), pp. 641-661.
A non-smooth regularization of a forward-backward parabolic equation
E. BonettiPrimo
;
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 propertyFile | Dimensione | Formato | |
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