The global attractor for the wave equation with nonlocal strong damping

Abstract

<p style='text-indent:20px;'>The paper is devoted to establishing the long-time behavior of solutions for the wave equation with nonlocal strong damping: <inline-formula><tex-math id="M1">\begin{document}$ u_{tt}-\Delta u-\|\nabla u_{t}\|^{p}\Delta u_{t}+f(u) = h(x). $\end{document}</tex-math></inline-formula> It proves the well-posedness by means of the monotone operator theory and the existence of a global attractor when the growth exponent of the nonlinearity <inline-formula><tex-math id="M2">\begin{document}$ f(u) $\end{document}</tex-math></inline-formula> is up to the subcritical and critical cases in natural energy space.</p>