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Approximate inertial manifolds for the pattern formation Cahn-Hilliard equation. (English) Zbl 0724.65122

Summary: An approximate inertial manifold for an evolution equation is a finite dimensional smooth manifold such that the orbits enter, after a transient time, a very thin neighbourhood of the manifold. In this paper, we consider the Cahn-Hilliard equation and we present a method which allows to construct several approximate inertial manifolds providing better and better order approximations to the orbits. These approximate inertial manifolds exist, whether an exact inertial manifold is known to exist or not.

MSC:

65Z05 Applications to the sciences
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
80A22 Stefan problems, phase changes, etc.
35Q72 Other PDE from mechanics (MSC2000)
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