Global attractor of the quasi-linear wave equation with strong damping

The paper investigates the existence of global attractor of the quasi-linear wave equation with strong damping utt−γΔut−Δu+f(u)=∇⋅ϕ′(∇u)+g. It proves that the energy solution of the equation is stable and the related dynamical system possesses a (strong) global attractor in natural energy space (rather than a weak one as known before). These results improve the recent ones in [13].