Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On behavior of solutions to a Petrovsky equation with damping and
  variable-exponent source   This paper deals with the following Petrovsky equation with damping and
nonlinear source \[u_{tt}+\Delta^2 u-M(\|\nabla u\|_2^2)\Delta u-\Delta
u_t+|u_t|^{m(x)-2}u_t=|u|^{p(x)-2}u\] under initial-boundary value conditions,
where $M(s)=a+ bs^\gamma$ is a positive $C^1$ function with parameters
$a>0,~b>0,~\gamma\geq 1$, and $m(x),~p(x)$ are given measurable functions. The
upper bound of the blow-up time is derived for low initial energy using the
differential inequality technique. For $m(x)\equiv2$, in particular, the upper
bound of the blow-up time is obtained by the combination of Levine's concavity
method and some differential inequalities under high initial energy. In
addition, by making full use of the strong damping, the lower bound of the
blow-up time is discussed. Moreover, the global existence of solutions and an
energy decay estimate are presented by establishing some energy estimates and
by exploiting a key integral inequality.

3
The categories of this paper are: physics
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
18
The categories of this paper are: econ