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Global attractor for the Cahn-Hilliard System. (English) Zbl 0803.35013
Summary: The Cahn-Hilliard system, a natural extension of the single Cahn-Hilliard equation in the case of multicomponent alloys, is shown to generate a dissipative semigroup on the phase space $${\mathcal H} = [H^ 2 (\Omega)]^ m$$. Following Hale’s ideas and based on the existence and form of the Lyapunov functional, our main result is the existence of a global attractor on a subset of $${\mathcal H}$$. New difficulties specific to the system case make our problem interesting.

##### MSC:
 35B40 Asymptotic behavior of solutions to PDEs 35K55 Nonlinear parabolic equations 35Q53 KdV equations (Korteweg-de Vries equations) 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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##### References:
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