Non-Linear Stability Analysis of Higher Order Dissipative Partial Differential Equations
Mathematical Physics
2007-05-23 v1 chao-dyn
Dynamical Systems
math.MP
Chaotic Dynamics
Pattern Formation and Solitons
patt-sol
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.
Cite
@article{arxiv.math-ph/9805014,
title = {Non-Linear Stability Analysis of Higher Order Dissipative Partial Differential Equations},
author = {J. -P. Eckmann and C. E. Wayne},
journal= {arXiv preprint arXiv:math-ph/9805014},
year = {2007}
}