Colli, Pierluigi; Gilardi, Gianni; Podio-Guidugli, Paolo; Sprekels, Jürgen Well-posedness and long-time behavior for a nonstandard viscous Cahn-Hilliard system. (English) Zbl 1331.74011 SIAM J. Appl. Math. 71, No. 6, 1849-1870 (2011). 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. Cited in 2 ReviewsCited in 21 Documents 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 Keywords:Cahn-Hilliard equation; phase field model PDFBibTeX XMLCite \textit{P. Colli} et al., SIAM J. Appl. Math. 71, No. 6, 1849--1870 (2011; Zbl 1331.74011) Full Text: DOI arXiv