MPEJ Volume 4, No.3, 20pp
Received: May 18, 1998, Revised: Jul 10, 1998, Accepted: Aug 5, 1998
J.-P. Eckmann, C.E. Wayne
Non-Linear Stability Analysis of Higher Order Dissipative Partial
Differential Equations
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.