The Cahn-Hilliard equation with dynamic boundary conditions

By Reinhard Racke, Songmu Zheng. Advances in Differential Equations, 2003

137 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Materials Chemistry, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eea4a3cd3b4f1bf006fb25747e97c22d045210f6

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Citations in the corpus

Two‐phase flows in karstic geometry (2014, unknown): “See for instance [41, 79, 80, 81].”
Maximal regularity and asymptotic behavior of solutions for the Cahn–Hilliard equation with dynamic boundary conditions (2006, background): “This was not proven in the previous work by [10].”
Exponential attractors for the Cahn–Hilliard equation with dynamic boundary conditions (2005, background): “The Cahn–Hilliard equation, endowed with dynamic boundary conditions, has been studied in References [9–12].”
On the Caginalp system with dynamic boundary conditions and singular potentials (2009, unknown): “In particular, the Cahn-Hilliard equation, endowedwiththeseboundaryconditions,hasbeenstudiedin[9],[12],[25],[26],[27], [ 28 ]and[32].”
A NUMERICAL ANALYSIS OF THE CAHN-HILLIARD EQUATION WITH DYNAMIC BOUNDARY CONDITIONS (2010, background): “From a mathematical point of view, problem (1)-(4) with an initial value has been studied in [3, 10, 11, 12, 20, 21, 22, 25].”
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).”
A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, methodology): “The approximate problem (3.7) can be locally solved by first analyzing its linearized problem and then applying the contraction mapping theorem (see [134, Theorem 3.1]).”
Convergence to steady states of solutions of the Cahn–Hilliard and Caginalp equations with dynamic boundary conditions (2006, background): “Using arguments similar to those in the proof of Theorem 2.1 in Prüss, Racke, and Zheng [17], we see that the operatorBq defined in Xq := H−1q′ (Ω) ×W 1−1/qq (Γ) by means of Bq(v, ρ) := (div∇∆u,−∆Γρ+ ∂νu) with domain D(Bq) = { (v, ρ) ∈ H3q (Ω) ×W 3−1/qq (Γ) : v|Γ = ρ } www.mn-journal.com c© 2006 WI”
On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions (2009, unknown): “3), has been studied in [7], [17], [28], [33], [34], and [37].”
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.”
Asymptotic behavior of a Cahn-Hilliard equation with Wentzell boundary conditions and mass conservation (2008, background): “Problem (1), (2), (10) supplemented with a no-flux boundary condition on the chemical potential μ = εut − ∆u + f (u) , ε ≥ 0 originated many mathematical papers devoted to various issues like well-posedness, regularity, and asymptotic behavior of solutions (see, for instance, [2, 25, 32, 34, 39], cf”
A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary Conditions (2014, result): “We just quote, among other contributions, [5, 18, 21, 23, 24, 28] and especially the papers [14] and [10].”