For a strongly continuous semigroup (T(t)) t 0 with generator A we introduce its critical spectrum \_ crit (T(t)). This yields in an optimal way the spectral mapping theorem \_(T(t))=e t\_(A) \_ \_ crit (T(t)) and improves classical stability results. 2000
On the Asymptotic Behavior of Perturbed Strongly Continuous Semigroups
โ Scribed by Simon Brendle
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 160 KB
- Volume
- 226
- Category
- Article
- ISSN
- 0025-584X
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๐ SIMILAR VOLUMES
In this paper we study the asymptotic behavior of the stability radius of a singularly perturbed system when the small parameter tends to zero. It is proved that for such systems the stability radius tends to the min(r , r ), where r is the inverse of the H -norm of the reduced slow model and r is t
## Abstract We consider the perturbed simple pendulum equation โ__u__ โณ(__t__) + __ฮผ__ |__u__ (__t__)|^__p__ โ1^__u__ (__t__) = __ฮป__ sin __u__ (__t__),โ__t__ โ __I__ โ (โ__T__, __T__), __u__ (__t__) > 0,โ__t__ โ __I__, __u__ (ยฑ__T__) = 0, where __p__ > 1 is a constant,__ฮป__ > 0 and __ฮผ__ โ **R