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

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

1998-05-15

arxiv.org/abs/math-ph/9805014v1

Physics

Mathematical Physics

Scientific paper

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.

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