Singular limit of an Allen-Cahn equation with nonlinear diffusion

DOI10.2140/tunis.2022.4.719OpenAlexW4316253718MaRDI QIDQ2683011

Perla El Kettani, Sunder Sethuraman, Hyunjoon Park, Danielle Hilhorst, Tadahisa Funaki

Publication date: 3 February 2023

Published in: Tunisian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.13081

zbMATH Keywords

mean curvature flowinterfacesurface tensionsingular limitnonlinear diffusionAllen-Cahn equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic equations (35K20) Comparison principles in context of PDEs (35B51) Quasilinear parabolic equations (35K59)

Related Items

Lecture Notes on the Singular Limit of Reaction-diffusion Systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the validity of formal asymptotic expansions in Allen-Cahn equation and FitzHugh-Nagumo system with generic initial data
• Dispersal towards food: the singular limit of an Allen-Cahn equation
• The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system
• Generation and propagation of interfaces for reaction-diffusion equations
• Interface motion in models with stochastic dynamics
• Motion by curvature in generalized Cahn-Allen models
• Existence for an Allen-Cahn/Cahn-Hilliard system with degenerate mobility
• Mean curvature interface limit from Glauber+Zero-range interacting particles
• Exponentially slow motion of interface layers for the one-dimensional Allen-Cahn equation with nonlinear phase-dependent diffusivity
• Generation of Interface for an Allen-Cahn Equation with Nonlinear Diffusion