Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A blow-up result for a generalized Tricomi equation with nonlinearity of
  derivative type   In this note, we prove a blow-up result for a semilinear generalized Tricomi
equation with nonlinear term of derivative type, i.e., for the equation
$\mathscr{T}_{\!\!\ell} u = |\partial_t u|^p$, where $ \mathscr{T}_{\!\!\ell} =
\partial_t^2-t^{2\ell}\Delta$. Smooth solutions blow up in finite time for
positive Cauchy data when the exponent $p$ of the nonlinear term is below
$\frac{\mathscr{Q}}{\mathscr{Q}-2}$, where $\mathscr{Q}=(\ell+1)n+1$ is the
quasi-homogeneous dimension of the generalized Tricomi operator
$\mathscr{T}_{\!\!\ell}$. Furthermore, we get also an upper bound estimate for
the lifespan.

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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol