Convective Cahn-Hilliard equation with degenerate mobility. (English) Zbl 1184.35176
This papers studies the existence of weak solutions for the convective Cahn-Hilliard equation with degenerate mobility. The main result is the existence of weak solutions.
For the proof, the authors establish the global existence of classical solutions for a regularized problem. Based on Schauder-type estimates uniform estimates are derived. These allow then to pass to the limit, and to establish the existence of weak solutions.
For the proof, the authors establish the global existence of classical solutions for a regularized problem. Based on Schauder-type estimates uniform estimates are derived. These allow then to pass to the limit, and to establish the existence of weak solutions.
Reviewer: Dirk Blömker (Augsburg)
MSC:
| 35K65 | Degenerate parabolic equations |
| 35G25 | Initial value problems for nonlinear higher-order PDEs |
| 35K55 | Nonlinear parabolic equations |
| 35D30 | Weak solutions to PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
