On continuity in parameters of integrated semigroups (Q1422536)

The author discusses the continuity in parameter \(\varepsilon\) of the integrated semigroup \(S(t,\varepsilon\)) generated by \(A(\varepsilon)\), \(\varepsilon\in P\), where \(P\) is a open set of a finite-dimensional normed linear space. He shows that if \(A(\varepsilon)x\) is strongly continuous with respect to \(\varepsilon\), then the integrated semigroup \(S(t,\varepsilon)\) is strongly continuous in \(\varepsilon\) uniformly on a bounded \(t\)-interval. As an example, the wave equation with damping boundary conditions is discussed.