Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical exponent of Fujita-type for the semilinear damped wave equation
  on the Heisenberg group with power nonlinearity   In this paper, we consider the Cauchy problem for the semilinear damped wave
equation on the Heisenberg group with power nonlinearity. We prove that the
critical exponent is the Fujita exponent $p_{\mathrm{Fuj}}(\mathscr{Q}) = 1+2 /
\mathscr{Q}$, where $\mathscr{Q}$ is the homogeneous dimension of the
Heisenberg group. On the one hand, we will prove the global existence of small
data solutions for $p >p_{\mathrm{Fuj}}(\mathscr{Q})$ in an exponential
weighted energy space. On the other hand, a blow-up result for $1 < p \leq
p_{\mathrm{Fuj}}(\mathscr{Q})$ under certain integral sign assumptions for the
Cauchy data by using the test function method.

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The categories of this paper are: eess
29
The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th