Title: Life-span of blowup solutions to semilinear wave equation with space-dependent critical damping,
Abstract: 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 $|x|^{-1}$.