In this paper,we first give a sufficient and necessary condition for M= to generate an exponentially bounded =-semigroup and discuss its relations to the C-wellposedness of the complete second order abstract Cauchy pr...In this paper,we first give a sufficient and necessary condition for M= to generate an exponentially bounded =-semigroup and discuss its relations to the C-wellposedness of the complete second order abstract Cauchy problem （（ACP<sub>2</sub>） for short） in some sense.Then we use these results and those in [1] to discuss the C-（exponential） wellposedness of a kind of （ACP<sub>2</sub>） with application backgrounds,and develop the results in [2].展开更多
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 cosin...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 a -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 function. The characterization of an exponentially bounded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.展开更多
基金This project is supported by the NNSF of Chinathe Youth Science and Technique Foundation of Shanxi Province China
文摘In this paper,we first give a sufficient and necessary condition for M= to generate an exponentially bounded =-semigroup and discuss its relations to the C-wellposedness of the complete second order abstract Cauchy problem （（ACP<sub>2</sub>） for short） in some sense.Then we use these results and those in [1] to discuss the C-（exponential） wellposedness of a kind of （ACP<sub>2</sub>） with application backgrounds,and develop the results in [2].
基金This project is supported by the Natural Science Foundation of China and Science Development Foundation of the Colleges and University of Shanghai.
文摘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 a -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 function. The characterization of an exponentially bounded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.
