On Two‐Parameter Regularized Semigroups and the Cauchy Problem

Mohammad Janfada

Abstract and Applied Analysis, 2009, vol. 2009, issue 1

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 (∂/(∂ti))u(t1, t2) = Hiu(t1, t2), i = 1, 2, ti > 0, u(0, 0) = x, x ∈ C(D(H1)∩D(H2)) is closely related to the two‐parameter C‐semigroups of operators.

Date: 2009
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https://doi.org/10.1155/2009/415847

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2009:y:2009:i:1:n:415847

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