Abstract and Applied Analysis

On Two-Parameter Regularized Semigroups and the Cauchy Problem

Mohammad Janfada

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Abstract

Suppose that X is a Banach space and C is an injective operator in B ( X ) , the space of all bounded linear operators on X . In this note, a two-parameter C -semigroup (regularized semigroup) of operators is introduced, and some of its properties are discussed. As an application we show that the existence and uniqueness of solution of the 2-abstract Cauchy problem ( / ( t i ) ) u ( t 1 , t 2 ) = H i u ( t 1 , t 2 ) , i = 1 , 2 , t i > 0 , u ( 0 , 0 ) = x , x C ( D ( H 1 ) D ( H 2 ) ) is closely related to the two-parameter C -semigroups of operators.

Article information

Source
Abstr. Appl. Anal., Volume 2009 (2009), Article ID 415847, 15 pages.

Dates
First available in Project Euclid: 16 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1268745585

Digital Object Identifier
doi:10.1155/2009/415847

Mathematical Reviews number (MathSciNet)
MR2533572

Zentralblatt MATH identifier
1200.47058

Citation

Janfada, Mohammad. On Two-Parameter Regularized Semigroups and the Cauchy Problem. Abstr. Appl. Anal. 2009 (2009), Article ID 415847, 15 pages. doi:10.1155/2009/415847. https://projecteuclid.org/euclid.aaa/1268745585


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