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We consider the Cahn-Hilliard equation on manifolds with conicalsingularities and prove existence of global attractors in higher orderMellin-Sobolev spaces with asymptotics. We also show convergence of solutionsin the same spaces to an equilibrium point and provide asymptotic behavior ofthe equilibrium near the conical tips in terms of the local geometry.

Existence of global attractors and convergence of solutions for the Cahn-Hilliard equation on manifolds with conical singularities