Well-posedness and long-time behavior for a nonstandard viscous Cahn--Hilliard system
- Colli, Pierluigi
- Gilardi, Gianni
- Podio-Guidugli, Paolo
- Sprekels, Jürgen
2010 Mathematics Subject Classification
- 74A15 35K55 35A05, 35B40
- Cahn-Hilliard equation, phase field model, well-posedness, long-time behavior
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.
- SIAM J. Appl. Math., 71 (2011) pp. 1849--1870.