Influence of corner layers in the variational determination of bubble solutions of the constrained Allen–Cahn equation

DOI10.1017/S0956792508007626zbMath1157.35310OpenAlexW2078012527MaRDI QIDQ3529505

M. C. Jorge, Carlos A. Vargas, Antonmaria A. Minzoni

Publication date: 13 October 2008

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0956792508007626

zbMATH Keywords

two-dimensional domainsharp interfacelimit of small diffusivityno-flux condition

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Singular perturbations in context of PDEs (35B25) Variational methods for second-order elliptic equations (35J20)

Cites Work

• Slow motion in the gradient theory of phase transitions via energy and spectrum
• Slow dynamics for the Cahn-Hilliard equation in higher space dimensions: The motion of bubbles
• The gradient theory of phase transitions and the minimal interface criterion
• The Gibbs-Thompson relation within the gradient theory of phase transitions
• A two-dimensional metastable flame-front and a degenrate spike-layer problem
• Fast Reaction, Slow Diffusion, and Curve Shortening
• A Variational Approach to Nonlinear Singularly Perturbed Boundary-Value Problems
• Motion of bubbles towards the boundary for the Cahn–Hilliard equation
• Metastable Bubble Solutions for the Allen-Cahn Equation with Mass Conservation
• An Asymptotic Analysis of Localized Solutions for Some Reaction‐Diffusion Models in Multidimensional Domains

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