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The Cahn-Hilliard Equation and the Allen-Cahn Equation on Manifolds with Conical Singularities
We consider the Cahn-Hilliard equation on a manifold with conical singularities. We first show the existence of bounded imaginary powers for suitable closed extensions of the bilaplacian. Combining results and methods from singular analysis with a theorem of Clément and Li we then prove the short time solvability of the …