Distribution cosine functions

Taiwanese Journal of Mathematics

Volumn 10, Issue 3, 2006, Pages 739-775

  Kostić, Marko ^a  

^a UNIVERSITY OF NOVI SAD   (Serbia)

Author keywords

Distribution cosine functions; Integrated cosine functions; Well posedness

Indexed keywords

EID: 33750060307     PISSN: 10275487     EISSN: 10275487     Source Type: Journal    
DOI: 10.11650/twjm/1500403859     Document Type: Article

References (24)

1. W. Arendt, O. El-Mennaoui and V. Keyantuo, Local integrated semigroups: evolution with the jumps of regularity, J. Math. Anal. Appl., 186 (1994), 572-595.
2. W. Arendt and H. Kellermann, Integrated solutions of Volterra integrodifferential equations and applications, Volterra integrodifferential equations in Banach spaces and applications, Proc. Conf., Trento/Italy 1987, Pitman Res. Notes Math. Ser., 190 (1989), 21-51.
3. W. Arendt, C. J. K. Batty, M. Hieber and F. Neubrander, Vector-valued Laplace Transforms and Cauchy Problems, Birkhäuser Verlag, 2001.
4. O. El-Mennaoui and V. Keyantuo, Trace theorems for holomorphic semigroups and the second order Cauchy problem, Proc. Amer. Math. Soc., 124 (1996), 1445-1458.
5. H. O. Fattorini, The Cauchy Problem, Addison-Wesley, 1983. MR 84g:34003.
6. V. Keyantuo, The Laplace transform and the ascent method for abstract wave equations, Journal of Differential Equations, 122 (1995), 27-47.
7. J. Kisyński, Distribution semigroups and one parameter semigroups, Bulletin of the Polish Academy of Sciences, 50 (2002), 189-216.
8. M. Kostić, C-distribution semigroups, Studia Math., to appear.
9. P. C. Kunstmann, Distribution semigroups and abstract Cauchy problems, Trans. Amer. Math. Soc., 351 (1999), 837-856.
10. P. C. Kunstmann, Stationary dense operators and generation of non-dense distribution semigroups, J. Operator Theory, 37 (1997), 111-120.
11. Y.-C. Li and S.-Y. Shaw, On generators of integrated C-semigroups and C-cosine functions, Semigroup Forum, 47 (1993), 29-35.
12. M. Li, F. Huang and Q. Zheng, Local integrated C-semigroups, Studia Math., 145 (2001), 265-280.
13. J. L. Lions, Semi-groups distributions, Portugal. Math., 19 (1960), 141-164.
14. I. V. Melnikova and A. Filinkov, Abstract Cauchy Problems: Three Approaches, Chapman Hall, Boca Raton, London, New York, Washington, 2001.
15. F. Neubrander, Integrated semigroups and their applications to complete second order Cauchy problems, Semigroup Forum, 38 (1989), 233-251.
16. S.-Y. Shaw, Cosine operator functions and Cauchy problems, Conferenze del Seminario Matematica dell'Universitá di Bari, Dipartimento Interuniversitario Di Matematica, 287, ARACNE, Roma, 2002, pp. 1-75.
17. S. Wang, Quasi-distribution semigroups and integrated semigroups, J. Funct. Anal., 146 (1997), 352-381.
18. S. W. Wang and Z. Huang, Strongly continuous integrated C-cosine operator functions, Studia Math., 126 (1997), 273-289.
19. T.-J. Xiao and J. Liang, The Cauchy Problem for Higher-Order Abstract Differential Equations, Lect. Notes in Math. Vol. 1701, Springer, 1998.
20. T. Xiao and J. Liang, Differential operators and C-wellposedness of complete second order abstract Cauchy problems, Pacific J. Math., 186 (1998), 167-191.
21. J. Zhang and Q. Zheng, On α-times integrated cosine functions, Mathematica Japonica, 50 (1999), 401-408.
22. Q. Zheng, Integrated cosine functions, Internat, J, Math. & Sci., 19, (1996), 575-580.
23. Q. Zheng and J. Zhang, Gaussian estimates and regularized groups, Proc. Amer. Math. Soc., 127 (1999), 1089-1096.
24. Q. Zheng, Coercive differential operators and fractionally integrated cosine functions, Taiwanese J. Math., 6 (2002), 59-65.