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