ASYMPTOTIC-BEHAVIOR OF C-0-SEMIGROUPS IN BANACH-SPACES

Authors
WEIS L WROBEL V
Citation
L. Weis et V. Wrobel, ASYMPTOTIC-BEHAVIOR OF C-0-SEMIGROUPS IN BANACH-SPACES, Proceedings of the American Mathematical Society, 124(12), 1996, pp. 3663-3671
Citations number
10
Categorie Soggetti
Mathematics, General",Mathematics,Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
124
Issue
12
Year of publication
1996
Pages
3663 - 3671
Database
ISI
SICI code
0002-9939(1996)124:12<3663:AOCIB>2.0.ZU;2-6
Abstract
We present optimal estimates for the asymptotic behavior of strongly c ontinuous semigroups U-A : [0, infinity[--> L(X) in terms of growth ab scissas of the resolvent function R(., A) of the generator A. In parti cular we give Ljapunov's classical stability condition a definite form for (infinite dimensional) abstract Cauchy problems: The abscissa of boundedness of R(., A) equals the growth bound of the classical soluti ons of y' = Ay.