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Mathematics > Analysis of PDEs

arXiv:1804.10638 (math)
[Submitted on 27 Apr 2018]

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

Authors: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.
Comments: 24pp
Subjects: Analysis of PDEs (math.AP)
MSC classes: 45K05, 35B40, 37L30, 35B36
Cite as: arXiv:1804.10638 [math.AP]
  (or arXiv:1804.10638v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.10638

Submission history

From: Joseph Shomberg [view email]
[v1] Fri, 27 Apr 2018 18:28:27 UTC (29 KB)
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