Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hele-Shaw flow as the sharp interface limit of the Cahn-Hilliard
  equation with disparate mobilities   In this paper, we study the sharp interface limit for solutions of the
Cahn-Hilliard equation with disparate mobilities. This means that the mobility
function degenerates in one of the two energetically favorable configurations,
suppressing the diffusion in that phase. First, we construct suitable weak
solutions to this Cahn-Hilliard equation. Second, we prove precompactness of
these solutions under natural assumptions on the initial data. Third, under an
additional energy convergence assumption, we show that the sharp interface
limit is a distributional solution to the Hele-Shaw flow with optimal
energy-dissipation rate.

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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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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: eess
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The categories of this paper are: hep-ph