Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Life-span of blowup solutions to semilinear wave equation with
  space-dependent critical damping   This paper is concerned with the blowup phenomena for initial value problem
of semilinear wave equation with critical space-dependent damping term
(DW:$V$). The main result of the present paper is to give a solution of the
problem and to provide a sharp estimate for lifespan for such a solution when
$\frac{N}{N-1}<p\leq p_S(N+V_0)$, where $p_S(N)$ is the Strauss exponent for
(DW:$0$). The main idea of the proof is due to the technique of test functions
for (DW:$0$) originated by Zhou--Han (2014, MR3169791). Moreover, we find a new
threshold value $V_0=\frac{(N-1)^2}{N+1}$ for the coefficient of critical and
singular damping $|x|^{-1}$.

20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat