Stochastic semigroups and coagulation equations

Ukrainian Mathematical Journal

Volumn 57, Issue 6, 2005, Pages 913-922

  Lachowicz, M ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27644542254     PISSN: 00415995     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11253-005-0239-y     Document Type: Article

References (22)

1. J. M. Ball and J. Carr, "The discrete coagulation-fragmentation equations: existence, uniqueness and density conservation," J. Statist. Phys., 61, 203-234 (1990).
2. F. Guias, Coagulation-Fragmentation Processes: Relations between Finite Particle Models and Differential Equations, Preprint 98-41 (SFB 359), Heidelberg (1998).
3. M. Lachowicz, P. Laurençot, and D. Wrzosek, "On the Oort-Hulst-Safronov coagulation equation and its relation to the Smoluchowski equation," SIAM J. Math. Anal., 34, No. 6, 1399-1421 (2003).
4. M. Lachowicz and D. Wrzosek, "A nonlocal coagulation-fragmentation model," Appl. Math. (Warsaw), 27, No. 1, 45-66 (2000).
5. M. Smoluchowski, "Versuch einer mathematischen Theorie der kolloiden Lösungen," Z. Phys. Chem., 92, 129-168 (1917).
6. M. Lachowicz and D. Wrzosek, "Nonlocal bilinear equations. Equilibrium solutions and diffusive limit," Math. Models Methods Appl. Sci., 11, 1375-1390 (2001).
7. E. Jäger and L. Segel, "On the distribution of dominance in a population of interacting anonymous organisms," SIAM J. Appl. Math., 52, 1442-1468 (1992).
8. L. Arlotti and N. Bellomo, "Population dynamics with stochastic interaction," Transp. Theory Statist. Phys., 24, 431-443 (1995).
9. L. Arlotti and N. Bellomo, "Solution of a new class of nonlinear kinetic models of population dynamics," Appl. Math. Lett., 9, 65-70 (1996).
10. L. Arlotti, N. Bellomo, and M. Lachowicz, "Kinetic equations modelling population dynamics," Transp. Theory Statist. Phys., 29, 125-139 (2000).
11. E. Geigant, K. Ladizhansky, and A. Mogilner, "An integrodifferential model for orientational distribution of F -Actin in cells," SIAM J. Appl. Math., 59, No. 3, 787-809 (1998).
12. M. Lachowicz, "From microscopic to macroscopic description for generalized kinetic models," Math. Models Methods Appl. Sci., 12, No. 7, 985-1005 (2002).
13. M. Lachowicz, "On bilinear kinetic equations. Between micro and macro descriptions of biological populations," Banach Center Publ., 63, 217-230 (2004).
14. M. Lachowicz, General Population Systems. Macroscopic Limit of a Class of Stochastic Semigroups (to appear).
15. M. Deaconu and N. Fournier, "Probabilistic approach of some discrete and continuous coagulation equation with diffusion," Stochast. Process. Appl., 101, 83-111 (2002).
16. P. Donnelly and S. Simons, "On the stochastic approach to cluster size distribution during particle coagulation," J. Phys. A: Math. Gen., 26, 2755-2767 (1993).
17. R. Lang and N. Xanh, "Smoluchowski's theory of coagulation in colloids holds rigorously in the Boltzmann-Grad limit," Z. Wahrscheinlichkeitstheor. r. Verw. Geb., 54, 227-280 (1980).
18. M. Lachowicz, "Describing competitive systems at the level of interacting individuals," Proc. Eighth Nat. Conf. Appl. Math. Biol. Medicine (Łajs, 25-28, Sept. 2002) (2002), pp. 95-100.
19. M. Lachowicz, "From microscopic to macroscopic descriptions of complex systems," Comp. Rend. Mecanique (Paris), 331, 733-738 (2003).
20. M. Lachowicz and M. Pulvirenti, "A stochastic particle system modeling the Euler equation," Arch. Ration. Mech. Anal., 109, No. 1, 81-93 (1990).
21. V. N. Kolokoltsov, "Hydrodynamic limit of coagulation-fragmentation type models of k-nary interacting particles," J. Statist. Phys. (to appear).
22. V. N. Kolokoltsov, "On extension of mollified Boltzmann and Smoluchowski equations to particle systems with a k-nary interaction," Rus. J. Math. Phys. (to appear).