Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blow-up solutions to the semilinear wave equation with a stylized
  pyramid as a blow-up surface   We consider the semilinear wave equation with subconformal power nonlinearity
in two space dimensions. We construct a finite-time blow-up solution with an
isolated characteristic blow-up point at the origin, and a blow-up surface
which is centered at the origin and has the shape of a stylized pyramid, whose
edges follow the bisectrices of the axes in $R^2$. The blow-up surface is
differentiable outside the bisecrtices. As for the asymptotic behavior in
similariy variables, the solution converges to the classical one-dimensional
soliton outside the bisectrices. On the bisectrices outside the origin, it
converges (up to a subsequence) to a genuinely two-dimensional stationary
solution, whose existence is a by-product of the proof.
  At the origin, it behaves like the sum of 4 solitons localized on the two
axes, with opposite signs for neighbors. This is the first example of a blow-up
solution with a characteristic point in higher dimensions, showing a really
two-dimensional behavior.
  Moreover, the points of the bisectrices outside the origin give us the first
example of non-characteristic points where the blow-up surface is
non-differentiable.

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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
34
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: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph