Semigroups for generalized birth-and-death equations in lp spaces

Semigroup Forum

Volumn 73, Issue 2, 2006, Pages 175-193

  Banasiak, Jacek ^a   Lachowicz, Miroslaw ^b   Moszynski, Marcin ^b  

^a UNIVERSITY OF KWAZULU NATAL   (South Africa)

^b UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846518955     PISSN: 00371912     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00233-006-0621-x     Document Type: Article

References (21)

1. Anderson, W. J., "Continuous-Time Markov Chains. An Applications-Oriented Approach", Springer-Verlag, New York 1991.
2. Banasiak, J., On multiple solutions to linear kinetic equations, Transport Theory Statist. Phys. 30(3-4) (2003), 367-384.
3. Banasiak, J., A complete description of dynamics generated by birth-and-death problems: a semigroup approach, "Mathematical Modelling of Population Dynamics" (R. Rudnicki, ed.), Banach Center Publications, vol. 63, 2004, pp. 165-176.
4. Banasiak, J. and M. Lachowicz, Topological chaos for birth-and-death-type models with proliferation, Math. Models Methods Appl. Sci. 12(6) (2002), 755-775.
5. Banasiak, J., M. Lachowicz and M. Moszyński, Chaotic behaviour of semigroups related to the process of gene amplification-deamplification with cells' proliferation, Math. Biosc. (in press).
6. Banasiak, J., M. Lachowicz and M. Moszyński, Topological chaos: when topology meets medicine, Appl. Math. Letters 16 (2003), 303-308.
7. Banasiak, J. and M. Moszyński, A generalization of Desch-Schappacher-Webb criteria for chaos, Discr. Cont. Dynam. Systems 12(5) (2005), 959-972.
8. Bailey, N. T., "The Elements of Stochatsic Processes with Application to the Natural Sciences", John Wiley & Sons, Inc, New York, 1964.
9. Chernoff, P. R., Perturbation of dissipative operators with relative bound one, Proceed. Amer. Math. Society 33(1) (1972), 72-74.
10. Janas, J. and M. Moszyński, Spectral properties of Jacobi matrices by asymptotic analysis, J. Approx. Theory 120 (2003), 309-336.
11. Kato, T., On the semi-groups generated by Kolmogoroff's differential equation, J. Math. Soc. Japan 6(1) (1954), 1-15.
12. Kato, T., "Perturbation Theory for Linear Operators", Springer-Verlag, New York, 1966.
13. Kimmel, M., A. Świerniak and A. Polański, Infinite-dimensional model of evolution of drug resistance of cancer cells, J. Math. Systems Estimation Control 8(1) (1998), 1-16.
14. Majorana, A. and C. Milazzo, Space homogeneous solutions of the linear semiconductor Boltzmann equation, J. Math. Anal. Appl. 259(2) (2001), 609-629.
15. Pazy, A., "Semigroups of Linear Operators and Applications to PDE", Springer-Verlag, New York, 1983.
16. Reuter, G. E. H. and W. Lederman, On differential equations for the transition probabilities of Markov processes with denumerably many states, Proc. Cambridge Phil. Soc. 49 (1953), 247-242.
17. Reuter, G. E. H., Denumerable Markov processes and the associated contraction semigroup, Acta Math. 97 (1957), 1-46.
18. Ricciardi, L. M., Stochastic population theory: birth and death processes, in: "Mathematical Ecology" (T. G. Hallamand and S. A. Levin, eds.), Springer-Verlag, Berlin, 1986, pp. 155-190.
19. Świerniak, A., A. Polański, M. Kimmel, A. Bobrowski and J. Śmieja, Qualitative analysis of controlled drug resistance model - inverse Laplace and semigroup approach, Control Cybernetics 28(1) (1999), 61-73.
20. Shubin, M. A., Pseudodifference operators and their Green function, Izv. Akad. Nauk SSSR Ser. Mat. 49(3) (1985), 662-671 (in Russian);
21. the English translation: Math. USSR-Izv. 26(3) (1986), 605-622.