  For the first order 1D $n\times n$ quasilinear strictly hyperbolic system
$\partial_tu+F(u)\partial_xu=0$ with $u(x, 0)=\varepsilon u_0(x)$, where
$\varepsilon>0$ is small, $u_0(x)\not\equiv 0$ and $u_0(x)\in C_0^2(\mathbb
R)$, when at least one eigenvalue of $F(u)$ is genuinely nonlinear, it is
well-known that on the finite blowup time $T_{\varepsilon}$, the derivatives
$\partial_{t,x}u$ blow up while the solution $u$ keeps to be small. For the 1D
scalar equation or $2\times 2$ strictly hyperbolic system (corresponding to
$n=1, 2$), if the smooth solution $u$ blows up in finite time, then the blowup
mechanism can be well understood (i.e., only the blowup of $\partial_{t,x}u$
happens). In the present paper, for the $n\times n$ ($n\geq 3$) strictly
hyperbolic system with a class of large initial data, we are concerned with the
blowup mechanism of smooth solution $u$ on the finite blowup time and the
detailed singularity behaviours of $\partial_{t,x}u$ near the blowup point. Our
results are based on the efficient decomposition of $u$ along the different
characteristic directions, the suitable introduction of the modulated
coordinates and the global weighted energy estimates.
