ArticleOriginal scientific text
Title
Strongly continuous integrated C-cosine operator functions
Authors 1, 1
Affiliations
- Department of Mathematics, Nanjing University, Nanjing, Jiangsu, 210093, P.R. China
Abstract
We extend some recent results for regularized semigroups to strongly continuous n-times integrated C-cosine operator functions. Several equivalent conditions for the existence and uniqueness of solutions of (ACP ) are also presented.
Bibliography
- [A] W. Arendt, Vector-valued Laplace transforms and Cauchy problems, Israel J. Math. 59 (1987), 327-352.
- [D] G. Da Prato, Semigruppi regolarizzabili, Ricerche Mat. 15 (1966), 223-248.
- [Dav-P] E. B. Davies and M. M. Pang, The Cauchy problem and a generalization of the Hille-Yosida theorem, Proc. London Math. Soc. 55 (1987), 181-208.
- [deL] R. deLaubenfels, Existence Families, Functional Calculi and Evolution Equations, Lecture Notes in Math. 1570, Springer, 1994.
- [del-P] R. deLaubenfels and S. Piskarev, Growth rate of cosine families, J. Math. Anal. Appl. 196 (1995), 442-451.
- [L-S1] Y.-C. Li and S.-Y. Shaw, On generators of integrated C-semigroups and C-cosine functions, Semigroup Forum 47 (1993), 29-35.
- [L-S2] Y.-C. Li and S.-Y. Shaw, Integrated C-cosine functions and the abstract Cauchy problem, preprint.
- [S-L1] S.-Y. Shaw and Y.-C. Li, On N-times integrated C-cosine functions, in: Evolution Equations, Marcel Dekker, New York, 1994, 393-406.
- [S-L2] S.-Y. Shaw and Y.-C. Li, N-times integrated C-semigroups and the abstract Cauchy problem, Taiwanese J. Math. 1 (1997), 75-102.
- [So] M. Sova, Cosine operator functions, Rozprawy Mat. 49 (1966), 1-47.
- [W-Wa] H. Wang and S. Wang, C-cosine operator functions and the applications to the second order abstract Cauchy problem, in: Functional Analysis in China, Kluwer Acad. Publ., Dordrecht, 1996, 333-350.
- [Wa] S. Wang, Mild integrated C-existence families, Studia Math. 112 (1995), 251-266.