Well-posedness and long-time behavior for a nonstandard viscous Cahn-Hilliard system
Please always quote using this URN:urn:nbn:de:0296-matheon-8179
- 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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| Author: | Pierluigi Colli, Gianni Gilardi, Paolo Podio-Guidugli, Jürgen Sprekels |
|---|---|
| URN: | urn:nbn:de:0296-matheon-8179 |
| Referee: | Fredi Tröltzsch |
| Document Type: | Preprint, Research Center Matheon |
| Language: | English |
| Date of first Publication: | 2011/04/27 |
| Release Date: | 2011/04/27 |
| Tag: | |
| Institute: | Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) |
| MSC-Classification: | 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B40 Asymptotic behavior of solutions |
| 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K55 Nonlinear parabolic equations | |
| 74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Axx Generalities, axiomatics, foundations of continuum mechanics of solids / 74A15 Thermodynamics | |
| Preprint Number: | 782 |
