C-Cosine functions and the abstract Cauchy problem, II

Journal of Mathematical Analysis and Applications

Volumn 210, Issue 2, 1997, Pages 647-666

  Kuo, Chung Cheng ^a   Shaw, Sen Yen ^a  

^a NATIONAL CENTRAL UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; FUNCTIONS; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

ABSTRACT CAUCHY PROBLEM; BANACH SPACE; COSINE FUNCTIONS;

MATHEMATICAL TECHNIQUES;

EID: 0031152515     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5421     Document Type: Article

References (12)

1. 1. J. M. Ball, Strongly continuous semigroups, weak solution and variation of constant formula, Proc. Amer. Math. Soc. 63 (1977), 370-373.
2. 2. H. O. Fattorini, Ordinary differential equations in linear topological spaces, I, J. Differential Equations 5 (1968), 72-105.
3. 3. H. O. Fattorini, Second order linear differential equations in Banach spaces, in "North-Holland Mathematics Studies," Vol. 108, North-Holland, Amsterdam, 1985.
4. 4. S. Kanda, Cosine families and weak solutions of second order differential equations, Proc. Japan Acad. Ser. A Math. Sci. 54 (1978), 119-123.
5. 5. C.-C. Kuo and S.-Y. Shaw, Local C-semigroups and the abstract Cauchy problem, preprint, 1993.
6. 6. C.-C. Kuo and S.-Y. Shaw, C-cosine functions and the abstract Cauchy problem, I, J. Math. Anal. Appl. 210 (1997), 632-646.
7. 7. Y.-C. Li, "Integrated C-Semigroups and C-Cosine Functions of Operators on Locally Convex Spaces," Ph.D. dissertation, National Central University, 1991.
8. 8. Y.-C. Li and S.-Y. Shaw, On generators of integrated C-semigroups and C-cosine functions, Semigroup Forum 47 (1993), 29-35.
9. 9. F. Neubrander, Well-posedness of abstract Cauchy problems, Semigroup Forum 29 (1984), 74-85.
10. 10. S.-Y. Shaw, On exponentially bounded C-cosine functions, preprint, 1992.
11. 11. S.-Y. Shaw and Y.-C. Li, On n-times integrated C-cosine functions, in "Evolution Equations," pp. 393-406, Dekker, New York, 1994.
12. 12. M. Sova, Cosine operator functions, Rozprawy Mat. 49 (1966), 1-47.