We consider in this article the Cahn-Hilliard equation endowed with dynamic boundary conditions. By interpreting these boundary conditions as a parabolic equation on the boundary and by considering a regularized problem, we obtain, by the Leray-Schauder principle, the existence and uniqueness of sol
✦ LIBER ✦
Maximal regularity and asymptotic behavior of solutions for the Cahn–Hilliard equation with dynamic boundary conditions
✍ Scribed by Jan Prüss; Reinhard Racke; Songmu Zheng
- Publisher
- Springer
- Year
- 2006
- Tongue
- English
- Weight
- 339 KB
- Volume
- 185
- Category
- Article
- ISSN
- 0373-3114
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## Abstract We consider a solution of the Cahn–Hilliard equation or an associated Caginalp problem with dynamic boundary condition in the case of a general potential and prove that under some conditions on the potential it converges, as __t__ → ∞, to a stationary solution. The main tool will be the
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