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- W4240164037 abstract "Publisher SummaryThe chapter presents a discussion on linear evolution operators. The chapter discusses a given family { – A(t)} of closed generators of strongly continuous semigroups on a Banach space X, and construct the associated evolution operators { U(t, s)}, under an assumption of quasistability on { A(t)}, certain continuity assumptions, as well as the similarity of this family to the perturbation family {A(t) + B(t)}, for an appropriately measurable family { B(t)} of bounded operators. The chapter summarizes the theorem containing the major result. It is sufficiently strong to cover the nonlinear applications where {A(t)} is typically stable on X and also stable on an appropriate dense smooth subspace Y. To avoid a needlessly technical development, the details of the construction is carried out, in the case where {A(t)} is stable on X and Y. The modifications required for quasi-stability are technical considerations of integration theory. In this chapter, X and Y are not assumed reflexive. The chapter discusses the validity of the formal representation of solutions of abstract linear Cauchy problems, and uses the classical example of a linear symmetric hyperbolic system to illustrate the concepts of the linear theory. This application, however, requires only the stability of {A( t ) }, not the more general notion of quasi-stability." @default.
- W4240164037 created "2022-05-12" @default.
- W4240164037 date "1983-01-01" @default.
- W4240164037 modified "2023-09-26" @default.
- W4240164037 title "Linear Evolution Operators" @default.
- W4240164037 doi "https://doi.org/10.1016/s0076-5392(08)60643-8" @default.
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