Convergence to Equilibrium for the Cahn-Hilliard Equation with Wentzell Boundary Condition

By Hao-qing Wu. 2004

76 citations recorded by the source corpus.

In this paper we consider the Cahn-Hilliard equation endowed with Wentzell boundary condition which is a model of phase separation in a binary mixture contained in a bounded domain with permeable wall. Under the assumption that the nonlinearity is analytic with respect to unknown dependent function, we prove the convergence of a global solution to an equilibrium as time goes to infinity by means of a suitable \L ojasiewicz-Simon type inequality with boundary term. Estimates of convergence rate are also provided.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/fe37aa986bfe5831d1917fbb7662b21a59b0a537

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In Applied Mathematics

In Computational Theory and Mathematics

In Materials Chemistry

Citations in the corpus

Asymptotic behavior of a Cahn-Hilliard equation with Wentzell boundary conditions and mass conservation (2008, methodology): “After establishing the above framework, it is standard to prove the lemma below (see for instance [2, 20, 39] and the references therein).”
A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, methodology): “They extended the argument in [78] and derived an extended Łojasiewicz–Simon inequality that also allows nonlinear term on the boundary, see [114, Proposition 6.1] (recall that in [78,144] only linear boundary conditions were considered).”
On the Caginalp system with dynamic boundary conditions and singular potentials (2009, background): “In particular, the Cahn-Hilliard equation, endowedwiththeseboundaryconditions,hasbeenstudiedin[9],[12],[25],[26],[27], [28]and[ 32 ].”
The Cahn-Hilliard Equation with Logarithmic Potentials (2011, unknown): “, [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.”
Convergence to equilibrium for the Cahn–Hilliard equation with a logarithmic free energy (2007, background): “[6], Hoffmann & Rybka [15], Prüss & Wilke [18], and Wu & Zheng [21].”