Strong Uniform Attractors for Nonautonomous Suspension Bridge-Type Equations

We discuss long-term dynamical behavior of the solutions for the nonautonomous suspension bridge-type equation in the strong Hilbert space D(A) x H-2(Omega) boolean AND H-0(1)(Omega), where the nonlinearity g(u, t) is translation compact and the time-dependent external forces h (x,t) only satisfy condition (C*) instead of translation compact. The existence of strong solutions and strong uniform attractors is investigated using a new process scheme. Since the solutions of the nonautonomous suspension bridge-type equation have no higher regularity and the process associated with the solutions is not continuous in the strong Hilbert space, the results are new and appear to be optimal.