On Local <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math>-Times Integrated <mml:math id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi></mml:math>-Semigroups

Li, Yuan-Chuan; Shaw, Sen-Yen

doi:https://doi.org/10.1155/2007/34890

Abstract and Applied Analysis

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Research Article | Open Access

Volume 2007 | Article ID 034890 | https://doi.org/10.1155/2007/34890

On Local α-Times Integrated C-Semigroups

Yuan-Chuan Li¹and Sen-Yen Shaw²

Academic Editor: Wolfgang Ruess

Received07 Nov 2006

Revised22 Apr 2007

Accepted20 Jul 2007

Published30 Aug 2007

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.

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Copyright

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.

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