The biharmonic heat operator on edge manifolds and non-linear fourth order equations

Boris Vertman

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arXiv · 1301.7299

The biharmonic heat operator on edge manifolds and non-linear fourth order equations

Boris Vertman

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Abstract

We construct the biharmonic heat kernel for a suitable self-adjoint extension of the bi-Laplacian on a manifold with incomplete edge singularities. We employ a microlocal description of the biharmonic heat kernel to establish mapping properties of the corresponding biharmonic heat operator on certain Banach spaces. This yields short time existence for a class of semi-linear equations of fourth order, including for example the Cahn-Hilliard equation. We also obtain asymptotics of the solutions near the edge singularity.

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Boris Vertman. 2013-01-30. The biharmonic heat operator on edge manifolds and non-linear fourth order equations. https://arxiv.org/abs/1301.7299

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