Asymptotic behavior of $C_0$-semigroups in Banach spaces
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- by Lutz Weis and Volker Wrobel PDF
- Proc. Amer. Math. Soc. 124 (1996), 3663-3671 Request permission
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 $y’=Ay$.References
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Additional Information
- Lutz Weis
- Affiliation: Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany
- MR Author ID: 181530
- Email: lutz.weis@math.uni-karlsruhe.de
- 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
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3663-3671
- MSC (1991): Primary 47D06
- DOI: https://doi.org/10.1090/S0002-9939-96-03373-4
- MathSciNet review: 1327051