On Two-Parameter Regularized Semigroups and the Cauchy Problem

被引：3
|
作者：
Janfada, Mohammad [1 ]
机构：
[1] Sabzevar Tarbiat Moallem Univ, Dept Math, Sabzevar, Iran
来源：
ABSTRACT AND APPLIED ANALYSIS | 2009年
关键词：
LOCAL C-SEMIGROUPS; COSINE FUNCTIONS;
D O I：
10.1155/2009/415847
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 (partial derivative/(partial derivative 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 is an element of C(D(H(1))boolean AND D(H(2))) is closely related to the two-parameter C-semigroups of operators. Copyright (C) 2009 Mohammad Janfada.
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页数：15
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