On Local α -Times Integrated C -Semigroups
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Abstract and Applied Analysis

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

Yuan-Chuan Li and Sen-Yen Shaw

Source: Abstr. Appl. Anal. Volume 2007 (2007), 18 pages.

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.

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aaa/1204126594
Digital Object Identifier: doi:10.1155/2007/34890


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