In this paper, we study nonautonomous Cauchy problems for a family of linear operators (A(t)) tβI on some Banach space X by means of evolution semigroups. In particular, we characterize "stability" in the so called "hyperbolic case" on the level of evolution semigroups and derive a product formula
β¦ LIBER β¦
Nonautonomous abstract Cauchy problems for strongly measurable families
β Scribed by Naoki Tanaka
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 293 KB
- Volume
- 274-275
- Category
- Article
- ISSN
- 0025-584X
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β¦ Synopsis
Abstract
This paper is devoted to the study of the inhomogeneous abstract Cauchy problem for timeβdependent linear evolution equation uβ²(t) = A(t)u(t) + f(t) for t β [0, T], under the strong measurability of A and a new type of quasiβstability condition from the viewpoint of the theory of finite difference approximations. (Β© 2004 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
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