Critical exponent for semi-linear structurally damped wave equation of
derivative type
Abstract
The main purpose of this paper is to study the following semi-linear
structurally damped wave equation with nonlinearity of derivative type:
$$u_{tt}- \Delta u+
\mu(-\Delta)^{\sigma/2}
u_t= |u_t|^p,\quad u(0,x)=
u_0(x),\quad u_t(0,x)=u_1(x),$$ with
$\mu>0$, $n\geq1$,
$\sigma \in (0,2]$ and
$p>1$. In particular, we are going to prove the
non-existence of global weak solutions by using a new test function and
suitable sign assumptions on the initial data in both the subcritical
case and the critical case.
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