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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 363089, 5 pages
http://dx.doi.org/10.1155/2014/363089
Research Article

A Parameter Property of Classical Solutions of Cauchy Problems

Kent State University at Trumbull, Warren, OH 44483, USA

Received 1 November 2013; Accepted 26 December 2013; Published 10 February 2014

Academic Editor: Yuming Xing

Copyright © 2014 Min He. 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 work is concerned with the abstract Cauchy problems that depend on parameters. The goal is to study continuity in the parameters of the classical solutions of the Cauchy problems. The situation considered in this work is when the operator of the Cauchy problem is not densely defined. By applying integrated semigroup theory and the results on continuity in the parameters of C0-semigroup and integrated semigroup, we obtain the results on the existence and continuity in parameters of the classical solutions of the Cauchy problems. The application of the obtained abstract results in a parabolic partial differential equation is discussed in the last section of the paper.