ASYMPTOTIC BEHAVIOR OF BOUNDED SOLUTIONS TO SOME SECOND ORDER EVOLUTION SYSTEMS

By using previous results of Rouhani [20-30] for dissipative systems, we study the asymptotic behavior of solutions to the following system of second order evolution equation {u ''(t) - cu'(t) is an element of Au(t) a.e. t is an element of (0, + infinity) u(0) = u0, sup(t >= 0) vertical bar u(t)vertical bar < + infinity where A is a maximal monotone operator in a real Hilbert space H and c >= 0. We investigate weak and strong convergence theorems for solutions to this system. Our results extend and unify previous results by Mitidieri [15] and Morosanu [17] who studied the case c = 0 by assuming that A is maximal monotone and A(-1)(0) not equal phi, as well as previous results by Veron [25] who studied the case c > 0 by assuming A to be strongly monotone.