An extension of Kato's stability condition for nonautonomous cauchy problems

Authors
Nickel, G Schnaubelt, R
Citation
G. Nickel et R. Schnaubelt, An extension of Kato's stability condition for nonautonomous cauchy problems, TAIWAN J M, 2(4), 1998, pp. 483-496
Citations number
11
Categorie Soggetti
Mathematics
Journal title
TAIWANESE JOURNAL OF MATHEMATICS
ISSN journal
10275487 → ACNP
Volume
2
Issue
4
Year of publication
1998
Pages
483 - 496
Database
ISI
SICI code
1027-5487(199812)2:4<483:AEOKSC>2.0.ZU;2-C
Abstract
An extension of Kato's stability condition for nonautonomous Cauchy problem s is presented. It is proved that in the commutative case this condition an d a mild regularity assumption imply wellposedness. If one supposes the Kat o-stability, then the solutions are given by an integral formula. By means of examples we show that in general these stability conditions cannot be om itted in our results. Moreover, it is seen that the Kato-stability is not n ecessary for wellposedness.