Abstract and Applied Analysis
Volume 2007 (2007), Article ID 34890, 18 pages
doi:10.1155/2007/34890
Research Article

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

Received 7 November 2006; Revised 22 April 2007; Accepted 20 July 2007

Academic Editor: Wolfgang Ruess

Copyright © 2007 Yuan-Chuan Li and Sen-Yen Shaw. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.