Internal layers intersecting the boundary of domain in the Allen-Cahn equation

DOI10.1007/BF03167411zbMath0987.35078OpenAlexW2009381301MaRDI QIDQ5950037

Toshiyuki Iibun, Kunimochi Sakamoto

Publication date: 13 June 2002

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03167411

zbMATH Keywords

mean curvature flowNeumann boundary value problembifurcationsasymptotic expansionsnumerical simulations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57)

Related Items (2)

Singular perturbation and bifurcation of diffuse transition layers in inhomogeneous media. II ⋮ Corner defects in almost planar interface propagation

Cites Work

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• On the asymptotic solutions for a weakly coupled elliptic boundary value problem with a small parameter
• The heat equation shrinking convex plane curves
• The heat equation shrinks embedded plane curves to round points
• Generation and propagation of interfaces for reaction-diffusion equations
• Existence of non-constant stable equilibria in competition-diffusion equations
• Critical spectrum and stability of interfaces for a class of reaction-diffusion equations
• Existence and stability of transition layers
• Local minimisers and singular perturbations
• Finite dimensional dynamics and interfaces intersecting the boundary: Equilibria and the quasi-invariant manifold
• Slow Dynamics of Interfaces in the Allen--Cahn Equation on a Strip-like Domain
• Stability of Stationary Interfaces with Contact Angle in a Generalized Mean Curvature Flow

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