  In the paper, we study the semilinear wave equation involving the nonlinear
damping $g(u_t) $ and nonlinearity $f(u)$. Under the wider ranges of exponents
of $g$ and $f$, the well-posedness of the weak solution is achieved by
establishing a priori space-time estimates. Then, the existence of the global
attractor in the naturally phase space $H^1_0(\Omega)\times L^2(\Omega)$ is
obtained. Moreover, we prove that the global attrator is regular, that is, the
global attractor is a bounded subset of $(H^2(\Omega)\cap H^1_0(\Omega))\times
H^1_0(\Omega)$.
