Asymptotic behavior of a Cahn-Hilliard equation with Wentzell boundary conditions and mass conservation

By Ciprian G. Gal, Hao Wu. 2008

49 citations recorded by the source corpus.

In this article, we consider a Cahn-Hilliard model with boundary conditions of Wentzell type and mass conservation. We show that each solution of this problem converges to a steady state as time goes to infinity, provided that the potential function $f$ is real analytic and satisfies certain growth assumptions. Estimates of the rate of convergence to equilibrium are obtained as well. We also recall some results about the existence of global and exponential attractors and their properties.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/1001486acfdb4abd9eef635a263230a5999d5144

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Materials Chemistry

Citations in the corpus

The Cahn-Hilliard Equation with Logarithmic Potentials (2011, background): “, [19], [35], [63], [65], [74], [76], [80], [82], [84], [140], [153], [157], [174], [175], [176], [177], [178], [180], [195], [204] and [216] for Neumann (or periodic) boundary conditions and to [51], [96], [97], [102], [170], [187], [190] and [210] for dynamic boundary conditions.”
A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, methodology): “To overcome the difficulty coming from a weaker dissipation, in [80] the authors made use of a generalized Poincaré inequality to derive an improved Lojasiewicz–Simon type inequality subject to certain mass constraint (see [80, Lemma 4.”