Open Access
2009 On Two-Parameter Regularized Semigroups and the Cauchy Problem
Mohammad Janfada
Abstr. Appl. Anal. 2009: 1-15 (2009). DOI: 10.1155/2009/415847


Suppose that X is a Banach space and C is aninjective operator in B(X), the space of all bounded linearoperators 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 (/(ti))u(t1,t2)=Hiu(t1,t2),i=1,2, ti>0, u(0,0)=x, xC(D(H1)D(H2)) is closely related to the two-parameter C-semigroups of operators.


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Mohammad Janfada. "On Two-Parameter Regularized Semigroups and the Cauchy Problem." Abstr. Appl. Anal. 2009 1 - 15, 2009.


Published: 2009
First available in Project Euclid: 16 March 2010

zbMATH: 1200.47058
MathSciNet: MR2533572
Digital Object Identifier: 10.1155/2009/415847

Rights: Copyright © 2009 Hindawi

Vol.2009 • 2009
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