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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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[2] DOI: 10.1063/1.1744102
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