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

TL;DR

This paper studies the long-term behavior of solutions to the Cahn-Hilliard equation on manifolds with conical singularities, proving the existence of global attractors and convergence to equilibrium with detailed asymptotics.

Contribution

It establishes the existence of global attractors and convergence results for the Cahn-Hilliard equation on manifolds with conical singularities, including asymptotic behavior analysis.

Findings

Existence of global attractors in Mellin-Sobolev spaces.

Solutions converge to equilibrium points.

Asymptotic behavior near conical tips characterized by local geometry.

Abstract

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