Spectral analysis of planar transition fronts for the Cahn-Hilliard equation

DOI10.1016/j.jde.2008.03.027zbMath1147.35058OpenAlexW1968200794MaRDI QIDQ932835

Peter Howard

Publication date: 11 July 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.03.027

zbMATH Keywords

Evans functionCahn-Hilliard equationspectral stabilityplanar transition front

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35) General topics in linear spectral theory for PDEs (35P05)

Related Items (10)

Stability of transition front solutions in multidimensional Cahn-Hilliard systems ⋮ Linear stability for transition front solutions in multidimensional Cahn-Hilliard systems ⋮ Asymptotic \(L^p\) stability for transition fronts in Cahn-Hilliard systems ⋮ Spectral analysis for periodic solutions of the Cahn-Hilliard equation on \(\mathbb R\) ⋮ Non-blow-up phenomenon for the Cahn-Hilliard equation with non-constant mobility ⋮ The spectral method for the Cahn-Hilliard equation with concentration-dependent mobility ⋮ Spectral Analysis for Stationary Solutions of the Cahn–Hilliard Equation in ℝ^d ⋮ Classical solutions for the Cahn-Hilliard equation with decayed mobility ⋮ Spectral analysis for transition front solutions in multidimensional Cahn-Hilliard systems ⋮ A gradient flow approach to relaxation rates for the multi-dimensional Cahn-Hilliard Equation

Cites Work

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• Asymptotic behavior near transition fronts for equations of generalized Cahn-Hilliard form
• Spectral comparison principles for the Cahn-Hilliard and phase-field equations, and time scales for coarsening
• Pointwise estimates on the Green's function for a scalar linear convection-diffusion equation
• Pointwise estimates and stability for dispersive-diffusive shock waves
• Pointwise Green's function bounds for multidimensional scalar viscous shock fronts
• Asymptotic behavior near planar transition fronts for the Cahn-Hilliard equation
• Pointwise Green's function estimates toward stability for multidimensional fourth-order viscous shock fronts
• Stability of the Travelling Wave Solution of the Fitzhugh-Nagumo System
• Pointwise semigroup methods and stability of viscous shock waves
• Asymptotic behavior of multidimensional scalar viscous shock fronts
• On the stability of the saddle solution of Allen–Cahn's equation
• Anomalous scaling for three‐dimensional Cahn‐Hilliard fronts

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