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On Exponential Stability ofC0Semigroups

✍ Scribed by Yue-Hu Luo; De-Xing Feng

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
174 KB
Volume
217
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this note, the exponential stability for C semigroups in a Hilbert space is 0 considered. First, an expression for a C semigroup is given, and then a formula on 0 the growth order of a C semigroup is obtained. Finally, with some additional 0 condition such as the boundedness of the resolvent of the generator of a C 0 semigroup on an imaginary axis, the exponential stability of a C semigroup is 0 proved.

πŸ“œ SIMILAR VOLUMES

On the Infinite Product ofC0-Semigroups
On the Infinite Product ofC0-Semigroups
✍ W Arendt; A Driouich; O El-Mennaoui πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 334 KB

Given a family (e tAk ) t 0 (k # N) of commuting contraction semigroups, we investigate when the infinite product > k=1 e tAk converges and defines a C 0 -semigroup. A particular case is the heat semigroup in infinite dimension introduced by Cannarsa and Da Prato (J. Funct. Anal. 118 (1993), 22 42).

On the Minimal Extension ofC0-Semigroups
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✍ Julio R Claeyssen; V Schuchman πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 153 KB

The present paper deals with a minimal extension of the classical semigroup theory for second-order damped differential equations in Banach spaces with closed, densely defined linear operators as coefficients. We do not ask anymore from our operators than in the case of first-order equations, i.e.,