Global attractor of thermoelastic coupled beam equations with structural damping (Q1992556)

Summary: In this paper, we study the existence of a global attractor for a class of \(n\)-dimension thermoelastic coupled beam equations with structural damping \(u_{t t} + \Delta^2 u + \Delta^2 u_t - [\sigma(\int_{\Omega} (\nabla u)^2 d x) + \phi(\int_{\Omega} \nabla u \nabla u_t d x)] \Delta u + f_1(u) + g(u_t) + \nu \Delta \theta = q(x)\), in \(\Omega \times R^+\), and \(\theta_t - \Delta \theta + f_2(\theta) - \nu \Delta u_t = 0\). Here \(\Omega\) is a bounded domain of \(R^N\), and \(\sigma(\cdot)\) and \(\phi(\cdot)\) are both continuous nonnegative nonlinear real functions and \(q\) is a static load. The source terms \(f_1(u)\) and \(f_2(\theta)\) and nonlinear external damping \(g(u_t)\) are essentially \(| u |^\rho u, | \theta |^{\varrho} \theta \), and \(| u_t |^r u_t\) respectively.