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Well-posedness and long-time behavior for a nonstandard viscous Cahn-Hilliard system. (English) Zbl 1331.74011

Summary: 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.

MSC:

74A15 Thermodynamics in solid mechanics
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35K25 Higher-order parabolic equations
35K59 Quasilinear parabolic equations
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