Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave
  System   We are concerned with rigorous mathematical analysis of shock diffraction by
two-dimensional convex cornered wedges in compressible fluid flow governed by
the nonlinear wave system. This shock diffraction problem can be formulated as
a boundary value problem for second-order nonlinear partial differential
equations of mixed elliptic-hyperbolic type in an unbounded domain. It can be
further reformulated as a free boundary problem for nonlinear degenerate
elliptic equations of second order. We establish a first global theory of
existence and regularity for this shock diffraction problem. In particular, we
establish that the optimal regularity for the solution is $C^{0,1}$ across the
degenerate sonic boundary. To achieve this, we develop several mathematical
ideas and techniques, which are also useful for other related problems
involving similar analytical difficulties.

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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con