## Abstract and Applied Analysis

### On Local $\alpha$-Times Integrated $C$-Semigroups

#### Abstract

This paper presents several characterizations of a local $\alpha$-times integrated $C$-semigroup $\{T(t); 0 \leq t \lt \tau\}$ by means of functional equation, subgenerator, and well-posedness of an associated abstract Cauchy problem. We also discuss properties concerning the nondegeneracy of $T(\cdot )$, the injectivity of $C$, the closability of subgenerators, the commutativity of $T(\cdot )$, and extension of solutions of the associated abstract Cauchy problem.

#### Article information

Source
Abstr. Appl. Anal., Volume 2007 (2007), Article ID 34890, 18 pages.

Dates
First available in Project Euclid: 27 February 2008

https://projecteuclid.org/euclid.aaa/1204126594

Digital Object Identifier
doi:10.1155/2007/34890

Mathematical Reviews number (MathSciNet)
MR2336261

Zentralblatt MATH identifier
1153.47035

#### Citation

Li, Yuan-Chuan; Shaw, Sen-Yen. On Local $\alpha$ -Times Integrated $C$ -Semigroups. Abstr. Appl. Anal. 2007 (2007), Article ID 34890, 18 pages. doi:10.1155/2007/34890. https://projecteuclid.org/euclid.aaa/1204126594

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