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Asymptotic behavior of $C_0$-semigroups in Banach spaces

Author(s): Lutz Weis; Volker Wrobel
Journal: Proc. Amer. Math. Soc. 124 (1996), 3663-3671.
MSC (1991): Primary 47D06
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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
Email: lutz.weis@math.uni-karlsruhe.de

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

DOI: 10.1090/S0002-9939-96-03373-4
PII: S 0002-9939(96)03373-4
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
Copyright of article: Copyright 1996, American Mathematical Society

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