Robust exponential attractors for Cahn‐Hilliard type equations with singular potentials

By Alain Miranville, Sergey Zelik. 2004

262 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/4ef119b781024182c42fa48033965e87265fa3b7

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In Applied Mathematics

In Computational Theory and Mathematics

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Citations in the corpus

The nonlocal Cahn–Hilliard equation with singular potential: Well-posedness, regularity and strict separation property (2017, methodology): “In particular, we are not able to argue as in [51] whose technique is based on a comparison principle for parabolic equations (see, e.”
Chapter 3 Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains (2008, result): “(d) Based on the above results, one has been able to prove the existence of exponential attractors in many situations, see [6,7,60,61,68,70,71,74,85,100–103,105–109,116, 117,157,175–177,184], and [216].”
Convergence to equilibrium for the Cahn–Hilliard equation with a logarithmic free energy (2007, methodology): “Further properties of the attractor were studied by Dupaix [8] and Miranville & Zelik [16].”
Exponential attractors for the Cahn–Hilliard equation with dynamic boundary conditions (2005, methodology): “Actually, following Reference [13], we regularize the problem by considering the viscous Cahn–Hilliard equation (see Reference [14]), i.”
Longtime behavior of nonlocal Cahn-Hilliard equations (2012, background): “This feature is an open problem even for the classical local Cahn-Hilliard equation with constant mobility in dimension three (see [37]).”
ASYMPTOTIC BEHAVIOR OF THE CAHN-HILLIARD-OONO EQUATION (2011, background): “Robust exponential attractors We first recall the following result concerning the construction of a robust family of exponential attractors for a discrete dynamical system (see [7]; see also [8], [10], [11], [12] and [13] for generalizations): Proposition 5.”
The Cahn-Hilliard Equation with Logarithmic Potentials (2011, methodology): “More details (and, in particular, the proofs of the results stated below) can be found in [169] and [173].”
A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, background): “In this direction, there is a huge literature on problem (1.1)–(1.4) and its variants, we refer to [24,27,42,44,45,54,55,58,59,101,136,138,140] and the references cited therein.”
On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions (2009, background): “, [1], [4], [7], [8], [10], [11], [12], [14], [17], [19], [23], [27], [28], [29], [30], [31], [32], [33], [34], [35], [37], and [38].”
Finite‐ and infinite‐dimensional attractors for porous media equations (2008, background): “6) (see, for example, [21]) which together with estimate (1.”
On the Cahn–Hilliard equation with dynamic boundary conditions and a dominating boundary potential (2014, background): “7), has drawn much attention in recent years: we quote, among other contributions, [6, 16, 18, 20, 21, 23].”
A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary Conditions (2014, background): “operator on Γ, W′ Γ is a nonlinearity analoguous to W ′ but now acting on the boundary value of the order parameter, and ﬁnally uΓ is a boundary source term. We just quote, among other contributions, [5,18,21,23,24,28] and especially the papers [14] and [10]. In the former, the reader can ﬁnd the ph”
A construction of a robust family of exponential attractors (2005, background): “In fact, in that case, the theorem is just a slight generalization of the abstract results contained in [4, 5, 10].”
Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems* (2005, background): “where C,� > 0 and distsymm denotes the symmetric Hausdorff distance; see also [13] and [ 21 ].”