On the evolution operator for a class of non-autonomous abstract parabolic equations (Q1206906)

The paper concerns the non-autonomous abstract parabolic equation \(u'(t)= A(t)u(t)+f(t)\), \(0< t\leq T\), where \(A(t)\) generates an analytic semigroup in a Banach space \(X\). Another major hypothesis is that \(D(A(t))\) and the interpolation spaces \(D_{A(t)}(\delta + 1,\infty)\) are supposed to be independent of \(t\) for some \(\delta \in (0,1)\).