Applications to linear, time-dependent evolution equations

Abstract

After developing the theory of linear and quasilinear (abstract) evolution equations in scales of Banach spaces we will give applications to linear and quasilinear pseudodifferential evolution equations in chapter 4 and 5. First, in the present chapter we describe several consequences for linear equations

$$u'\left( t \right) = A\left( t \right)u\left( t \right) + f\left( t \right).$$