Integrated semigroups and their application to complete second order Cauchy problems (Q1262521)

The author studies well posedness of the complete second order Cauchy problem \[ u''(t)-Bu'(t)-Au(t)=0;\quad u(0)=x,\quad u'(0)=y. \] The main concept of the paper is ``biclosedness'' of the pair A, B. That means \(P(\lambda)=\lambda^ 2I-\lambda B-A\) with domain \(D(P)(\lambda)=D(A)\cap D(B)\) is closed for all \(\lambda >w\). Of course estimations concerning the resolvent \(R_{\lambda}=P^{-1}(\lambda)\) also play a crucial role.