Long time behavior of the strongly damped wave equation with p-laplacian in R?

Abstract

In this paper, the initial value problem for the one dimensional strongly damped wave equation with p-Laplacian and localized damping in the whole space is concerned. Under the condition 2 < p < 4, the existence of weak local attractors for this problem in (W¹, ? (R) ? H¹ (R) x L² (R) is proved.