ABSTRACT
Our interest when developing scattering theories is centred mainly on initial value problems (IVP) and initial boundary value problems (IBVP) associated with such equations as the wave equation, that is, with equations which are of second order in time. We have seen in Chapter 3 that such equations can be reduced, at least in formal manner, to a system of equations which are of first order in time. It turns out that for these first order equations, results concerning existence, uniqueness and stability can be obtained in an efficient and elegant manner by using the theory of semigroups. To fix ideas let H denote a Hilbert space and consider the IBVP represented by d ψ ( t ) d t − G ψ ( t ) = 0 , t ∈ R + , ψ ( 0 ) = ψ 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137254/d7974a1f-d94d-4722-b5ac-945336cfa90a/content/eq966.tif"/>
