Well-posedness and Global Attractors for Viscous Fractional Cahn-Hilliard Equations with Memory

Eylem Öztürk; Joseph L. Shomberg

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arXiv · 1804.10638

Well-posedness and Global Attractors for Viscous Fractional Cahn-Hilliard Equations with Memory

Eylem Öztürk·Joseph L. Shomberg

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Abstract

We examine a viscous Cahn-Hilliard phase-separation model with memory and where the chemical potential possesses a nonlocal fractional Laplacian operator. The existence of global weak solutions is proven using a Galerkin approximation scheme. A continuous dependence estimate provides uniqueness of the weak solutions and also serves to define a precompact pseudometric. This, in addition to the existence of a bounded absorbing set, shows that the associated semigroup of solution operators admits a compact connected global attractor in the weak energy phase space. The minimal assumptions on the nonlinear potential allow for arbitrary polynomial growth.

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Eylem Öztürk, Joseph L. Shomberg. 2018-04-27. Well-posedness and Global Attractors for Viscous Fractional Cahn-Hilliard Equations with Memory. https://arxiv.org/abs/1804.10638

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