As is well known, it is possible to describe the long time behavior of many dissipative systems generated by evolution PDEs of mathematical physics in terms of so-called global attractors, i.e., compact invariant set in the phase space attracting the images of all bounded subsets under the temporal evolution. Therefore, it can be deduced that the global attractor (if exists) includes all of the nontrivial dynamics. In this talk, I first give some abstract results on the existence of such an attractor. Then, as an application, I prove the existence of a regular strong global attractor of a 1-dimensional strongly damped wave equation with p-Laplacian term in the space W01,p (0, 1)× L2(0, 1)