Convergence to equilibrium for the Cahn–Hilliard equation with a logarithmic free energy

By Helmut Abels, M. Wilke. 2007

175 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/557df1a4eb21d738216add9a54576557e1cdb97c

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In Applied Mathematics

In Computational Theory and Mathematics

In Materials Chemistry

Citations in the corpus

A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, methodology): “…a monotone operator plus a globally Lipschitz continuous one, they achieved the conclusion in a direct manner by solving an abstract Cauchy problem for a suitable Lipschitz perturbation of a monotone operator, which is the subgradient of the convex part of the energy E bulk (see [65, Theorem 3.1]).”
Isogeometric analysis of the Cahn–Hilliard phase-field model (2008, background): “The behavior of the stationary solutions in multidimensions is not well understood [1,14,17].”
Critical spaces for quasilinear parabolic evolution equations and applications (2017, background): “It has been subject of intensive research during the last decades, see for instance [1, 6, 9] and the references therein.”
On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions (2009, unknown): “We refer the reader, among a vast literature, to, e.g., [ 1 ], [4], [7], [8], [10], [11], [12], [14], [17], [19], [23], [27], [28], [29], [30], [31], [32], [33], [34], [35], [37], and [38].”
The Cahn-Hilliard Equation with Logarithmic Potentials (2011, background): “This is established in [3], for the physically relevant logarithmic potentials, by using the analyticity of f and a proper version of the SimonLojasiewicz inequality (note that such a result is not trivial, as, when the space dimension n is greater than 2, there may be continua of steady states).”
The nonlocal Cahn–Hilliard equation with singular potential: Well-posedness, regularity and strict separation property (2017, background): “The global-in-time higher-order estimate in V established here is not enough to apply a compactness argument as in [3] to recover the result about the convergence to a single stationary state.”