东华大学学报(英文版)
東華大學學報(英文版)
동화대학학보(영문판)
JOURNAL OF DONGHUA UNIVERSITY
2001年
1期
51-54
,共4页
α-times integrated regularized cosine function%mild α-times integrated C-existence family of second order%C-wellposed%second order abstract Cauchy problem
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 finction.The characterization of an exponentially botnded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.
