A SPECTRAL MAPPING THEOREM FOR SEMIGROUPS SOLVING PDEs WITH NONAUTONOMOUS PAST
نویسنده
چکیده
for an evolution family (U(t, s))t≤s≤0 on X . We refer to [5, 12] where these equations have been introduced and to [10, 13] for concrete examples. In particular, we showed in [12] that (1.1) and the abstract Cauchy problem associated to an operator ( ,D( )) on the product space := X × L(R−,X) are “equivalent.” Since, under appropriate conditions, the operator ( ,D( )) is the generator of a strongly continuous semigroup ( (t))t≥0 on , the solutions of (1.1) can be obtained from this semigroup (see [12, Theorem 3.5]).
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