Upper semicontinuity of an attractor of a singularly perturbed hyperbolic equation (Q1908421)

Consider the singularly perturbed hyperbolic equation \[ \partial^2_t u + \partial_t u = - \varepsilon \Delta^2 u + \Delta u - f(u) - g(x) \] with initial and boundary conditions \(u |_{t = 0} = u_0 (x)\), \(\partial_t u |_{t = 0} = p_0 (x)\), \(u |_{\partial \Omega} = \Delta u |_{\partial \Omega} = 0\). The main result of the present paper is a theorem on the convergence of the attractor of the perturbed problem to the attractor of the limiting problem.