Non-Linear Stability Analysis of Higher Order Dissipative Partial Differential Equations

1998/05/15 by Jean‐Pierre Eckmann, J. -P. Eckmann, C. Eugene Wayne +3 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS) #Stability and Controllability of Differential Equations #chao-dyn #math-ph #math.DS #math.MP #nlin.CD #nlin.PS #patt-sol

paper · pdf · doi:10.48550/arxiv.math-ph/9805014

arxiv created 1998/05/15 · openalex publication_date 1998/05/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the invariant manifold method for analyzing the asymptotics of dissipative partial differential equations on unbounded spatial domains to treat equations in which the linear part has order greater than two. One important example of this type of equation which we analyze in some detail is the Cahn-Hilliard equation. We analyze the marginally stable solutions of this equation in some detail. A second context in which such equations arise is in the Ginzburg-Landau equation, or other pattern forming equations, near a codimension-two bifurcation.

Citations

• Free Energy of a Nonuniform System. I. Interfacial Free Energy

Cited by

• Invariant Manifolds and the Long-Time Asymptotics of the Navier-Stokes and Vorticity Equations on R 2

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