In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems on a Banach space by the existence of certain evolution semigroups.
Then, we use these generation results for evolution semigroups to derive wellposedness for nonautonomous Cauchy problems under some “concrete” conditions. As a typical example, we discuss the so called “parabolic” case.
"Evolution semigroups for nonautonomous Cauchy problems." Abstr. Appl. Anal. 2 (1-2) 73 - 95, 1997. https://doi.org/10.1155/S1085337597000286