Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Short Time Existence for Coupling of Scaled Mean Curvature Flow and
  Diffusion   We prove a short time existence result for a system consisting of a geometric
evolution equation for a hypersurface and a parabolic equation on this evolving
hypersurface. More precisely, we discuss a mean curvature flow scaled with a
term that depends on a quantity defined on the surface coupled to a diffusion
equation for that quantity. The proof is based on a splitting ansatz, solving
both equations separately using linearization and a contraction argument. Our
result is formulated for the case of immersed hypersurfaces and yields a
uniform lower bound on the existence time that allows for small changes in the
initial value of the height function.

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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio