Exponential attractors for the Cahn–Hilliard equation with dynamic boundary conditions

By Alain Miranville, Sergey Zelik. 2005

153 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/4e9174a48e1adee3db3e8e13c5861b3253846262

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Citations in the corpus

On the Caginalp system with dynamic boundary conditions and singular potentials (2009, methodology): “Following[14],[ 25 ],weintroduceafurthervariable ψ = u| andviewthedynamic boundary condition as a parabolic equation for ψon the boundary, namely,”
A Cahn–Hilliard model in bounded domains with permeable walls (2006, background): “Thus, arguing as in [5], [16], [17], we can extend the above result to the case when the norm of X is replaced by H(2)(Ω)×H(2)(Γ).”
A NUMERICAL ANALYSIS OF THE CAHN-HILLIARD EQUATION WITH DYNAMIC BOUNDARY CONDITIONS (2010, background): “2 in [20] shows that there exists at most one solution (u,w) of (10)-(11) satisfying (25): the computations are valid because the solution is regular enough.”
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].”
The Cahn-Hilliard Equation with Logarithmic Potentials (2011, background): “The existence, uniqueness and regularity of the solution uk to this regularized problem is clear, since the nonlinear term is now regular (see [170]).”
Null controllability for parabolic equations with dynamic boundary conditions of reactive-diffusive type (2013, background): “The well-posedness and regularity results for the underlying evolution equations rely on this fact, which mainly follows from a result in [27].”
A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, methodology): “A third approach to study problem (3.5) was given in [129], where the authors considered the viscous Cahn–Hilliard equation for α ≥ 0: where F , G ∈ C 3 ( R ) are some general (but regular) potentials with arbitrary growth and satisfy the following dissipative conditions: They introduced a new…”
Long time behavior of the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions (2010, background): “The Cahn-Hilliard system, endowed with these boundary conditions, has been studied in [6, 18, 23, 24, 26, 27] (see also [4–6, 12–15, 17] for similar boundary conditions for the Caginalp phase-field system).”
Asymptotic behavior of a Cahn-Hilliard equation with Wentzell boundary conditions and mass conservation (2008, background): “Besides, the problem has also been analyzed as a dissipative dynamical system in [25], where the main result is the construction of a family of exponential attractors which is robust with respect to the viscosity coefficient ε.”
On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions (2009, background): “3), has been studied in [7], [17], [28], [33], [34], and [37].”