Strong attractors for weakly damped quintic wave equation in bounded domains (Q2097559)

This paper deals with global attractors of the wave equation defined in a smooth bounded domain \(\Omega\) in \(\mathbb{R}^3\): \[ u_{tt} +\gamma u_t -\Delta u + f(u) =g, \quad t>0, \ x\in \Omega, \] with boundary condition \[ u(t,x) =0, \quad t>0, \ x\in \partial \Omega, \] and initial data \[ u(0,x) =u_0(x), \quad u_t(0,x) = u_1(x), \quad x\in \Omega, \] where \(\gamma>0\) is a constant, \(g\in L^2(\Omega)\), and \(f\) is a nonlinear function with quintic growth rate. Under further dissipativeness and growth conditions, the authors prove the existence of finite-dimensional global attractors of the equation in \(H^2(\Omega) \bigcap H^1_0(\Omega) \times H^1_0(\Omega)\).