BIFURCATIONS OF INVARIANT MANIFOLDS OF THE CONVECTIVE CAHN-HILLIARD EQUATION

摘要

We consider the periodic boundary value problem for the convective Cahn–Hilliard equation in the case where the unknown function depends on two spatial variables. We obtain sufficient conditions for the existence and stability of two- and three-dimensional invariant manifolds. We deduce asymptotic formulas for the solutions. We show that the three-dimensional invariant manifold is a one-parameter family of two-dimensional invariant tori containing tori with ergodic and resonance dynamics simultaneously.