On an extension of the Kato-Voigt perturbation theorem for substochastic semigroups and its application

Taiwanese Journal of Mathematics

Volumn 5, Issue 1, 2001, Pages 169-191

  Banasiak, J ^a  

^a UNIVERSITY OF KWAZULU NATAL   (South Africa)

Author keywords

Fragmentation model; Perturbation theory for semigroups; Substochastic semigroup

Indexed keywords

EID: 0001038023     PISSN: 10275487     EISSN: None     Source Type: Journal    
DOI: 10.11650/twjm/1500574893     Document Type: Article

References (14)

1. L. Arlotti, The Cauchy problem for the linear Maxwell-Boltzmann equation, J. Differential Equations 69 (1987), 166-184.
2. 1spaces with applications to transport equations and Kolmogorov's differential equations, Acta Appl. Math. 23 (1991), 129-144.
3. J. Banasiak, Mathematical properties of inelastic scattering models in kinetic theory, Math. Moddls Methods Appl. Sci. 10 (2000), 163-186.
4. J. Banasiak, On a diffusion-kinetic equation arising in extended kinetic theory, Math. Methods Appl. Sci. 23(14) (2000), 1237-1256.
5. K.-J. Engel, R. Nagel, One-parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, Springer Verlag, New York, 1999.
6. T. Kato, On the semi-groups generated by Kolmogoroff's differential equations, J. Math. Soc. Japan 6 (1954), 1-15.
7. W. Lamb, private communication.
8. D. J. McLaughlin, W. Lamb and A. C. McBride, A semigroup approach to fragmentation models, SIAM J. Math. Anal. 28 (1997), 1158-1172.
9. M. Mokhtar-Kharroubi, Mathematical Topics in Neutron Theory: New Aspects, World Scientific, Singapore, 1997.
10. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, 1983.
11. H. Risken, The Fokker-Planck Equation, 2nd ed., Springer Verlag, Berlin, 1989.
12. H. H. Schaefer, Banach Lattices and Positive Operators, Springer Verlag, New York, 1974.
13. 0-semigroups and their generators, Transport Theory Statist. Phys. 16 (1987), 453-466.
14. R. M. Ziff and E. D. McGrady, The kinetics of cluster fragmentation equation and polymerization, J. Phys. A 18 (1985), 3027-3037.