Maximal regularity and asymptotic behavior of solutions for the Cahn–Hilliard equation with dynamic boundary conditions

By Jan Prüss, Reinhard Racke, Songmu Zheng. 2006

105 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/8dc8476a9cc3bcc6e76bf2b32c138cebe028c04e

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In Applied Mathematics

In Computational Theory and Mathematics

In Materials Chemistry

Citations in the corpus

A Cahn–Hilliard model in bounded domains with permeable walls (2006, methodology): “Now, let us consider the Cahn–Hilliard equation that was extensively studied in References [9–13].”
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.”
A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, background): “…paper [132], the authors studied the maximal L p -regularity of the system (see [132, Theorem 2.1]) and provided an alternative proof on the global well-posedness of problem (3.5) (see [132, Theorem 4.1]), which further implies that the solution indeed defines a C 0 -semigroup in V 1 as expected.”
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].”
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].”
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].”
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).”
Inhomogeneous symbols, the Newton polygon, and maximal Lp-regularity (2008, background): “, [23], [22] for the Cahn-Hilliard equation) and boundary value problems with dynamic boundary conditions ([10], [8]).”
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].”