Some remarks on the asymptotic behaviour of the solutions of second order evolution equations (Q1076891)

We study the asymptotic behaviour as \(t\to \infty\) of the solution of u''\(\in Au\), \(u(0)=u_ 0\), \(\sup_{t>0}\| u(t)\| <+\infty,\) where A is a maximal monotone operator in a real Hilbert space H, and \(u_ 0\) belongs to the domain of A. Using a suitable geometric hypothesis on A, we prove (via an ergodic result due to Brezis-Browder) strong convergence of the solution as \(t\to +\infty\). The existence of solutions with compact support is also considered.