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Integrated semigroups and their application to complete second order Cauchy problems. (English) Zbl 0686.47038
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.
Reviewer: J.de Graaf

MSC:
47D03 Groups and semigroups of linear operators
47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
34G10 Linear differential equations in abstract spaces
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