Generation of Interface for Solutions of the Mass Conserved Allen--Cahn Equation

DOI10.1137/18M1204747zbMath1447.35029OpenAlexW3034127873MaRDI QIDQ5119980

Hendrik Weber, Hiroshi Matano, Thanh Nam Nguyen, Danielle Hilhorst

Publication date: 9 September 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1204747

zbMATH Keywords

generation of interfacenonlocal integral termabsence of interfaceno use of comparison principles

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Free boundary problems for PDEs (35R35) Semilinear parabolic equations (35K58) Integro-partial differential equations (35R09)

Related Items (1)

On the large time behavior of the solutions of a nonlocal ordinary differential equation with mass conservation

Cites Work

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• Convergence to steady state for the solutions of a nonlocal reaction-diffusion equation
• On the large time behavior of the solutions of a nonlocal ordinary differential equation with mass conservation
• Mass conserving Allen-Cahn equation and volume preserving mean curvature flow
• Intermediate dynamics of internal layers for a nonlocal reaction-diffusion equation
• The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system
• Asymptotic behavior and stability of solutions of semilinear diffusion equations
• Generation and propagation of interfaces for reaction-diffusion equations
• Instability results for reaction-diffusion equations with Neumann boundary conditions
• Dynamical approximation of internal transition layers in a bistable nonlocal reaction-diffusion equation via the averaged mean curvature flow
• Nonlocal reaction—diffusion equations and nucleation
• Geometrical Evolution of Developed Interfaces

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