Well-posedness and long-time behavior for a nonstandard viscous Cahn-Hilliard system

Details Well-posedness and long-time behavior for a nonstandard viscous Cahn-Hilliard system Well-posedness and long-time behavior for a nonstandard viscous Cahn-Hilliard system

2011-03-23

arxiv.org/abs/1103.4585v1

Mathematics

Analysis of PDEs

Key words: Cahn-Hilliard equation, phase field model, well-posedness, long-time behavior

Scientific paper

We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a careful development of uniform estimates and the deduction of certain useful boundedness properties, we prove existence and uniqueness of a global-in-time smooth solution to the associated initial/boundary-value problem; moreover, we give a description of the relative omega-limit set.

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