*(English)*Zbl 0646.34006

The paper can be considered as a review, in which - on the basis of certain assumptions - a unified approach to abstract linear nonautonomous parabolic equations is proposed. In particular, the linear parabolic Cauchy problem

is studied in a Banach space E, with $x\in E$ and f:[0,T]$\to E$ as prescribed data. In (1) $\{$ A(t)$\}$ $t\in [0,T]$ is a family of closed linear operators in E which are generators of analytic semigroups, and whose domain ${D}_{A\left(t\right)}$ may change with t and be not dense in E. Existence, uniqueness and regularity results are illustrated. The paper consists of 7 sections, rich in definitions, lemmas, propositions and theorems. In the last section examples and comparisons with the available literature are discussed.

##### MSC:

34A12 | Initial value problems for ODE, existence, uniqueness, etc. of solutions |