The global attractor for the wave equation with nonlocal strong damping

Abstract

The paper is devoted to establishing the long-time behavior of solutions for the wave equation with nonlocal strong damping: utt − ∆u − ∇ut p ∆ut + f (u) = h(x). It proves the well-posedness by means of the monotone operator theory and the existence of a global attractor when the growth exponent of the nonlinearity f (u) is up to the subcritical and critical cases in natural energy space.