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

Abstract

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 ∇u and the chemical potential Δus′(u). The existence is shown using a newly developed generalization of gradient flows by the author and the theory of Young measures.

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Correspondence to Martin Heida.

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Heida, M. Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation. Appl Math 60, 51–90 (2015). https://doi.org/10.1007/s10492-015-0085-7

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Keywords

  • Cahn-Hilliard
  • anisotropic behavior
  • gradient flow
  • curve of maximal slope
  • entropy

MSC 2010

  • 35D30
  • 35K57
  • 47J35
  • 80A22