Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vanishing diffusion in a dynamic boundary condition for the
  Cahn-Hilliard equation   The initial boundary value problem for a Cahn-Hilliard system subject to a
dynamic boundary condition of Allen-Cahn type is treated. The vanishing of the
surface diffusion on the dynamic boundary condition is the point of emphasis.
By the asymptotic analysis as the diffusion coefficient tends to 0, one can
expect that the solutions of the surface diffusion problem converge to the
solution of the problem without the surface diffusion. This is actually the
case, but the solution of the limiting problem naturally looses some
regularity. Indeed, the system we investigate is rather complicate due to the
presence of nonlinear terms including general maximal monotone graphs both in
the bulk and on the boundary. The two graphs are related each to the other by a
growth condition, with the boundary graph that dominates the other one. In
general, at the asymptotic limit a weaker form of the boundary condition is
obtained, but in the case when the two graphs exhibit the same growth the
boundary condition still holds almost everywhere.

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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg