  In this paper we focus on the initial value problem for quasi-linear
dissipative plate equation in multi-dimensional space $(n\geq2)$. This equation
verifies the decay property of the regularity-loss type, which causes the
difficulty in deriving the global a priori estimates of solutions. We overcome
this difficulty by employing a time-weighted $L^2$ energy method which makes
use of the integrability of $\|(\p^2_xu_t,\p^3_xu)(t)\|_{L^{\infty}}$. This
$L^\infty$ norm can be controlled by showing the optimal $L^2$ decay estimates
for lower-order derivatives of solutions. Thus we obtain the desired a priori
estimate which enables us to prove the global existence and asymptotic decay of
solutions under smallness and enough regularity assumptions on the initial
data. Moreover, we show that the solution can be approximated by a
simple-looking function, which is given explicitly in terms of the fundamental
solution of a fourth-order linear parabolic equation.
