Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The biharmonic heat operator on edge manifolds and non-linear fourth
  order equations   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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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: stat