Strong global attractors for 3D wave equations with weakly damping (Q437559)

Summary: The authors consider the existence of the global attractor \(\mathcal A_1\) for the 3D weakly damped wave equation. They prove that \(\mathcal A_1\) is compact in \((H^2(\Omega) \cap H^1_0(\Omega)) \times H^1_0(\Omega)\) and attracts all bounded subsets of \((H^2(\Omega) \cap H^1_0(\Omega)) \times H^1_0(\Omega)\) with respect to the norm of \((H^2(\Omega) \cap H^1_0(\Omega)) \times H^1_0(\Omega)\). Furthermore, this attractor coincides with the global attractor in the weak energy space \(H^1_0(\Omega) \times L^2(\Omega)\).