Is there any literature corresponding to one or two-parameter semigroups such that e.g. $T(t) \in \mathcal{L}(X(t))$ or $T(s,t) \in \mathcal{L}(X(t),X(s))$ for parameterized Banach spaces $X(t)$?

I have only seen the case where $X(t) \equiv X$ (i.e. there is only one Banach space).

This may be useful for PDE problems where there are moving domains.