Evolution semigroups for nonautonomous Cauchy problems

Gregor Nickel

Abstract and Applied Analysis, 1997, vol. 2, issue 1-2, 73-95

Abstract: In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems (NCP) {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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https://doi.org/10.1155/S1085337597000286

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2:y:1997:i:1-2:p:73-95

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