Geodesic
Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation
Applications of Mathematics, Tome 60 (2015) no. 1, pp. 51-90 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.1007/s10492-015-0085-7
Classification : 35D30, 35K57, 47J35, 80A22
Keywords: Cahn-Hilliard; anisotropic behavior; gradient flow; curve of maximal slope; entropy 
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Heida, Martin. Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation. Applications of Mathematics, Tome 60 (2015) no. 1, pp. 51-90. doi: 10.1007/s10492-015-0085-7

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