A semidiscrete scheme for a one-dimensional Cahn–Hilliard equation

By Carina Geldhauser, Matteo Novaga. 2011

381 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/c225c4a9e7bbc4856cc42e565883f8b734f8e3a6

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In Computational Mechanics

In Computational Theory and Mathematics

In Materials Chemistry

Citations in the corpus

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.”
An Adaptive Time-Stepping Strategy for the Cahn-Hilliard Equation (2012, background): “Elliott and Zheng proved the existence and uniqueness of the solution for the Cahn-Hilliard equation in [6].”
Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentials (2015, background): “1 Introduction The Cahn–Hilliard equation [5,14] yields a famous description of the evolution phenomena on the solid-solid phase separation.”
Iterative methods for solving fourth‐ and sixth‐order time‐fractional Cahn‐Hillard equation (2019, background): “(20) If we choose u0, h,L , and (x, t) properly so that Equation (19) converges at q = 1 n , then from Equation (18), we obtain”
On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions (2009, neutral): “, [1], [4], [7], [8], [10], [11], [12], [14], [17], [19], [23], [27], [28], [29], [30], [31], [32], [33], [34], [35], [37], and [38].”
A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, methodology): “This case appeared in the original derivation of the Cahn– Hilliard equation [1] and a thermodynamically reasonable choice is M ( s ) = 1 − s 2 (see [4, 23, 67, 68]).”
On the Cahn–Hilliard equation with dynamic boundary conditions and a dominating boundary potential (2014, neutral): “1 Introduction The classical Cahn–Hilliard equation and the so-called viscous Cahn–Hilliard equation (see [4, 10, 11]) in their simplest forms read ∂ty −∆w = 0 and w = τ∂ty −∆y + β(y) + π(y)− g in Ω× (0, T ), (1.”