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On the abstract Cauchy problem in the case of constant domains. (English) Zbl 0589.34047

The authors study the existence, unicity and regularity of the classical, strict and strong solutions \(u\in C([0,T];E)\) of the evolution non- autonomous equation \(u'(t)-A(t)u(t)=f(t)\) with the initial value \(u(0)=x\in E\) (E is a Banach space). The operators A(t) are infinitesimal generators of analytic semigroups and they have the domain independent of t, not necessarily dense in E. The necessary and sufficient conditions are formulated guaranteeing the existence and Hölder-continuity of the solution and its derivative.
Reviewer: O.John

MSC:

34G10 Linear differential equations in abstract spaces
47D03 Groups and semigroups of linear operators
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