The Cahn-Hilliard equation and the Biharmonic heat kernel on edge manifolds
Boris Vertman · arXiv (Cornell University) · 2013
We construct the biharmonic heat kernel of a suitable closed self-adjoint extension of the bi-Laplacian on a manifold with incomplete edge singularities. We establish mapping properties of the biharmonic heat operator and derive short time existence for certain semi-linear equations of fourth order. We apply the analysis to a class of semi-linear partial differential equations in particular the Cahn-Hilliard equation and obtain asymptotics of the solutions near the edge singularity.