Γ-type estimates for the one-dimensional Allen–Cahn’s action

DOI10.3233/ASY-151308zbMath1325.49018OpenAlexW2175070667MaRDI QIDQ3195643

Al-hassem Nayam, Giovanni Bellettini, Matteo Novaga

Publication date: 20 October 2015

Published in: Asymptotic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3233/asy-151308

zbMATH Keywords

singular perturbations\(\varGamma\)-expansionAllen-Cahn action functionals

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Singular perturbations in context of PDEs (35B25) Methods involving semicontinuity and convergence; relaxation (49J45) Asymptotic expansions of solutions to PDEs (35C20)

Related Items (10)

Slow motion for one-dimensional nonlinear damped hyperbolic Allen-Cahn systems ⋮ Slow motion for the 1D Swift-Hohenberg equation ⋮ On a conjecture of De Giorgi about the phase-field approximation of the Willmore functional ⋮ Slow motion for a hyperbolic variation of Allen–Cahn equation in one space dimension ⋮ Second order asymptotic development for the anisotropic Cahn-Hilliard functional ⋮ Slow motion for the nonlocal Allen-Cahn equation in \(n\) dimensions ⋮ Second-order \(\Gamma\)-limit for the Cahn-Hilliard functional ⋮ Sharp interface limit of a multi-phase transitions model under nonisothermal conditions ⋮ Existence of periodic orbits near heteroclinic connections ⋮ Periodic motions for multi-wells potentials and layers dynamic for the vector Allen-Cahn equation

Cites Work

• Slow motion for gradient systems with equal depth multiple-well potentials
• Gamma-convergence of gradient flows on Hilbert and metric spaces and applications
• Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy
• Asymptotic expansions by \(\Gamma \)-convergence
• On the two-phase Stefan problem with interfacial energy and entropy
• Slow-motion manifolds, dormant instability, and singular perturbations
• \(\Gamma\)-asymptotic developments, the Cahn-Hilliard functional, and curvatures
• Asymptotic development by \(\Gamma{}\)-convergence
• Gamma-convergence of gradient flows with applications to Ginzburg-Landau
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)

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