In this paper we discuss a family of viscous Cahn{Hilliard equations with a non-smooth viscosity term. This system may be viewed as an approximation of a "forward-backward" parabolic equation. The resulting problem is highly nonlinear, coupling in the same equation two nonlinearities with the diffusion term. In particular, we prove existence of solutions for the related initial and boundary value problem. Under suitable assumptions, we also state uniqueness and continuous dependence on data.
A doubly nonlinear cahn-hilliard system with nonlinear viscosity / E. Bonetti, P. Colli, L. Scarpa, G. Tomassetti. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 17:3(2018), pp. 1001-1022. [10.3934/cpaa.2018049]
A doubly nonlinear cahn-hilliard system with nonlinear viscosity
E. Bonetti
;
2018
Abstract
In this paper we discuss a family of viscous Cahn{Hilliard equations with a non-smooth viscosity term. This system may be viewed as an approximation of a "forward-backward" parabolic equation. The resulting problem is highly nonlinear, coupling in the same equation two nonlinearities with the diffusion term. In particular, we prove existence of solutions for the related initial and boundary value problem. Under suitable assumptions, we also state uniqueness and continuous dependence on data.
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