Evolution semigroups for nonautonomous Cauchy problems

Gregor Nickel

Abstract and Applied Analysis, 1997, vol. 2, 1-23

Abstract:

In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems ( N C P ) { u ˙ ( t ) = A ( t ) u ( t ) u ( s ) = x ∈ X on a Banach space X 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.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:632147

DOI: 10.1155/S1085337597000286

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