Title

A Parameter Property of Classical Solutions of Cauchy Problems

Publication Title

Abstract & Applied Analysis

Publication Date

2-2014

Document Type

Article

DOI

10.1155/2014/363089

Keywords

cauchy problem, semigroups (algebra), parabolic differential equations, mathematical models, integral operators

Disciplines

Analysis | Applied Mathematics | Mathematics

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 ofC0-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.


Share

COinS