Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hele-Shaw problem as a "Mesa" limit of Stefan problems: Existence,
  uniqueness, and regularity of the free boundary   We study a Hele-Shaw problem with a mushy region obtained as a Mesa type
limit of one phase Stefan problems in exterior domains. We study the
convergence, determine some of the qualitative properties and regularity of the
unique limiting solution, and prove regularity of the free boundary of this
limit under very general conditions on the initial data. Indeed, our results
handle changes in topology and multiple injection slots.

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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-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