PULLBACK ATTRACTORS FOR A CLASS OF NON-AUTONOMOUS THERMOELASTIC PLATE SYSTEMS

In this article we study the asymptotic behavior of solutions, in the sense of pullback attractors, of the evolution system {u(tt) + Delta(2)u + a(t)Delta theta = f(t,u), t > tau, x is an element of Omega, theta(t) + kappa Delta theta + a(t)Delta u(t) = 0, t > tau, x is an element of Omega, subject to boundary conditions u = Delta u= theta = 0, t > tau, x is an element of partial derivative Omega, where Omega is a bounded domain in R-N with N >= 2, which boundary partial derivative Omega is assumed to be a C-4-hypersurface, kappa > 0 is constant, a is an Holder continuous function and f is a dissipative nonlinearity locally Lipschitz in the second variable. Using the theory of uniform sectorial operators, in the sense of P. Sobolevskii ([23]), we give a partial description of the fractional power spaces scale for the thermoelastic plate operator and we show the local and global well-posedness of this non-autonomous problem. Furthermore we prove existence and uniform boundedness of pullback attractors.