A Hartman-Grobman theorem for the Cahn-Hilliard and phase-field equations

DOI10.1007/BF02219190zbMath0795.35052MaRDI QIDQ1319927

Peter W. Bates, Kening Lu

Publication date: 12 May 1994

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

zbMATH Keywords

structural stabilityCahn-Hilliard equationinvariant foliationsinertial manifoldHartman-Grobman theoremphase-field equationsexponentially small solutions

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (15)

The Hartman-Grobman theorem for semilinear hyperbolic evolution equations ⋮ Topological decoupling and linearization of nonautonomous evolution equations ⋮ Invariant foliations for \(C^1\) semigroups in Banach spaces ⋮ Optimal estimates for the uncoupling of differential equations ⋮ Finite dimensional aspects of semilinear parabolic equations ⋮ On the Hartman-Grobman theorem with parameters ⋮ Convergence of Solutions to a Convective Cahn–Hilliard-Type Equation of the Sixth Order in Case of Small Deposition Rates ⋮ Linearization for difference equations with infinite delay ⋮ Local Theory for Spatio-Temporal Canards and Delayed Bifurcations ⋮ The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension ⋮ On discretizations of invariant foliations over inertial manifolds ⋮ Time-averaging under fast periodic forcing of parabolic partial differential equations: Exponential estimates ⋮ Inertial manifolds and normal hyperbolicity ⋮ A unified approach to compute foliations, inertial manifolds, and tracking solutions ⋮ Invariant foliations near normally hyperbolic invariant manifolds for semiflows

Cites Work

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• Invariant manifolds for flows in Banach spaces
• Structural stability on two-dimensional manifolds
• An introduction to infinite dimensional dynamical systems -- geometric theory. With an appendix by Krzysztof P. Rybakowski
• On the singular limit in a phase field model of phase transitions
• Spectral comparison principles for the Cahn-Hilliard and phase-field equations, and time scales for coarsening
• Structured phase transitions on a finite interval
• The Morse-Smale property for a semilinear parabolic equation
• Inertial manifolds for nonlinear evolutionary equations
• Slow motion for the Cahn-Hilliard equation in one space dimension
• A Hartman-Grobman theorem for scalar reaction-diffusion equations
• Smooth invariant foliations in infinite dimensional spaces
• Inertial manifolds and inertial sets for the phase-field equations
• Smoothness of inertial manifolds
• Structural stability of \(C^1\) diffeomorphisms
• Metastable patterns for the Cahn-Hilliard equation. I
• Metastable patterns for the Cahn-Hilliard equation. II: Layer dynamics and slow invariant manifold
• On a theorem of Anosov
• On Morse-Smale dynamical systems
• Structurally Stable Systems are not Dense
• On a Theorem of P. Hartman
• Differentiable dynamical systems
• On structural stability

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