α-times Integrated Regularized Cosine Functions and Second Order Abstract Cauchy Problems

作     者：Zhang Jizhou(张寄洲) Tao Youshan(陶有山) 

作者机构：College of Mathematics Science Shanghai Normal University Shanghai 200234 Department of Applied Mathematics Dong Hua University Shanghai 200051 

出 版 物：《Journal of Donghua University(English Edition)》 (东华大学学报（英文版）)

年 卷 期：2001年第18卷第1期

页      面：51-54页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This project is supported by the Natural Science Foundation of China and Science Development Foundation of the Colleges and University of Shanghai 

主　　题：α-times integrated regularized cosine function, mild α-times integrated C-existence family of second order, C-wellposed, second order abstract Cauchy problem. 

摘      要：In this paper, α -times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α -times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α + 1)-times abstract Cauchy problem and mild α -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine *** characterization of an exponentially botnded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.