Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation

[摘要] We show existence of solutions to two types of generalized anisotropic Cahn-Hilliard problems: In the first case, we assume the mobility to be dependent on the concentration and its gradient, where the system is supplied with dynamic boundary conditions. In the second case, we deal with classical no-flux boundary conditions where the mobility depends on concentration $u$, gradient of concentration $\nabla u$ and the chemical potential $\Delta u-s'(u)$. The existence is shown using a newly developed generalization of gradient flows by the author and the theory of Young measures.

[学科分类] 应用数学

[关键词] Cahn-Hilliard;anisotropic behavior;gradient flow;curve of maximal slope;entropy