Published online by Cambridge University Press: 05 May 2022
In this chapter, we study internally well-posed systems. An internally well-posed i/s/o system is a resolvable i/s/o system whose main operator is the generator of a C0 semigroup, and an internally well-posed s/s system is a s/s system that has at least one internally wellposed i/s/o representation. Most of the results that we present for these classes of i/s/o and s/s systems are based on the results on resolvable i/s/o and s/s systems presented in Chapters 11 and 12. Internally well-posed systems are uniquely solvable, but they need not have the continuation property, and in the time-domain study of these systems the notions of a classical trajectory is more important than the notion of a generalized or mild trajectory. Many of the basic transformations and interconnections of i/s/o and s/s systems discussed in earlier chapters have the property that they preserve internal well-posedness.