Asymptotic behavior of bounded solutions to some second order evolution systems
From the abstract: By using previous results of Rouhani for dissipative systems, we study the asymptotic behavior of solutions to the following second order evolution equation \[ u''(t)-cu'(t)\in Au(t),\qquad u(0)=u_0, \qquad \sup_{t\geq 0} |u(t)|<+\infty , \] where \(A\) is a maximal monotone operator in a real Hilbert space \(H\) and \(c\geq 0\). We investigate weak and strong convergence theorems for solutions to this system. Our results extend and unify previous results by Mitidieri and by Morosanu who studied the case \(c=0\) by assuming that \(A\) is maximal monotone and \(A^{-1}(0)\not= \emptyset\), as well as previous results by Veron who studied the case \(c>0\) by assuming \(A\) to be strongly monotone.
scientific article; zbMATH DE number 5779829