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Abstract: . Let (A(t)) t0 and (B(t)) t0 be two families of closed operators satisfying the Acquistapace-Terreni conditions or the Kato-Tanabe conditions, or assumptions of maximal regularity, and let (U(t; s)) t>s0 and (V (t; s)) t>s0 be the associated evolution families. We obtain some estimates for kU(t; s) V (t; s)k in terms of A( ) 1 B( ) 1 for s t. We deduce some results showing that if A( ) 1 B( ) 1 ! 0 suciently quickly as !1 then U and V have similar asymptotic ... (Update)
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...Thm.5.6.1] see also [15] for closely related facts and [30] for further references. Very recently, C.J.K. Batty and R. Chill showed in [5] that one can allow for ff = 0 in (1.2) i.e. convergence in L(X) This paper extends [30] in several directions, e.g. the almost...
.... with almost periodic A( are treated in, e.g. 8] and [10] for X = C and in [13] for a certain class of parabolic problems, see also [5], 15] 17] For general evolution families U (but subject to an extra condition not assumed here) it is shown in [14] that U has an...
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BibTeX entry: (Update)
C.J.K. Batty, R. Chill, Approximation and asymptotic behaviour of evolution families, preprint. http://citeseer.ist.psu.edu/438639.html More
@misc{ batty-approximation,
author = "C. Batty and R. Chill",
title = "Approximation and asymptotic behaviour of evolution families",
text = "C.J.K. Batty, R. Chill, Approximation and asymptotic behaviour of evolution
families, preprint.",
url = "citeseer.ist.psu.edu/438639.html" }
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