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

Dept. of Mathematics, Boston University, 111 Cummington St., Boston, MA 02215, USAAbstract. We extend the invariant manifold method for analyzing the asymptotics of dissipative partial differentialequations on unbounded spatial domains to treat equations in which the linear part has order greater than two. Oneimportant example of this type of equation which we analyze in some detail is the Cahn-Hilliard equation. We analyzethe marginally stable solutions of this equation in some detail. A second context in which such equations arise is in theGinzburg-Landau equation, or other pattern forming equations, near a codimension-two bifurcation.