Linear Equations of Parabolic Type
Wolf von Wahl · 1985
In this chapter we want to discuss linear equations of parabolic type in a Banach space B, this means equations of the form $$\begin{array}{*{20}{c}} {u' + A\left( t \right)u = f,} \\ {u\left( O \right) = \varphi ,} \\ \end{array}$$ where each -A(t) generates an analytic semigroup in B. As for the domain of definition D(A(t)) of A(t) we concentrate on the time-independent case, namely D(A(t)) =D(A(0)). The basic material will be put together only briefly since it is common part now of many well known textbooks, e.g. [F], [Y1], [Ta], [Kr].