Abstract and Applied Analysis
Volume 2007 (2007), Article ID 34890, 18 pages
doi:10.1155/2007/34890
On Local α-Times Integrated C-Semigroups
Yuan-Chuan Li1
and Sen-Yen Shaw2
1Department of Applied Mathematics, National Chung-Hsing University, Taichung 402, Taiwan
2Graduate School of Engineering, Lunghwa University of Science and Technology, Taoyuan 333, Taiwan
Abstract
This paper presents several characterizations of a local α-times integrated C-semigroup {T(t);0≤t<τ} by means of functional equation, subgenerator, and well-posedness of an associated abstract Cauchy problem. We also discuss properties concerning the nondegeneracy of T(⋅), the injectivity of C, the closability of subgenerators, the commutativity of T(⋅), and extension of solutions of the associated abstract Cauchy problem.