Long-term behavior for wave equation with nonlinear damping and super-cubic nonlinearity

In this paper, we consider the semilinear wave equation involving the nonlinear damping term $g(u_t)$ and nonlinearity $f(u)$. The well-posedness of the weak solution satisfying some additional regularity is achieved under the wider ranges of the exponents $g$ and $f$. Moreover, the existence of global attractor and exponential attractor are proved.