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Asymptotic behavior of $C_0$-semigroups
in Banach spaces

Authors: Lutz Weis and Volker Wrobel
Journal: Proc. Amer. Math. Soc. 124 (1996), 3663-3671
MSC (1991): Primary 47D06
MathSciNet review: 1327051
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Abstract | References | Similar Articles | Additional Information

Abstract: We present optimal estimates for the asymptotic behavior of
strongly continuous semigroups $U_A:[0,\infty [\rightarrow L(X)$ in terms of growth abscissas of the resolvent function $R(\cdot ,A)$ of the generator $A$. In particular we give Ljapunov's classical stability condition a definite form for (infinite dimensional) abstract Cauchy problems: The abscissa of boundedness of $R(\cdot ,A)$ equals the growth bound of the classical solutions of $y'=Ay$.

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Additional Information

Lutz Weis
Affiliation: Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany

Volker Wrobel
Affiliation: Mathematisches Seminar, Universität Kiel, D-24098 Kiel, Germany

Received by editor(s): January 17, 1995
Additional Notes: The first author was supported by the Louisiana Education Quality Support Fund (LEQSF-RD-A-O8).
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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