On a Kinetic Equation for Coalescing Particles

Communications in Mathematical Physics

Volumn 246, Issue 2, 2004, Pages 237-267

  Escobedo, Miguel ^a   Laurençot, Philippe ^b   Mischler, Stéphane ^c,d  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^b INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^c UNIVERSITÉ DE VERSAILLES SAINT QUENTIN EN YVELINES   (France)

^d INRIA ROCQUENCOURT   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2142819302     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1037-3     Document Type: Article

References (40)

1. Aldous, D.J.: Deterministic and stochastic models for coalescence (aggregation, coagulation): A review of the mean-field theory for probabilists. Bernoulli 5, 3-48 (1999)
2. Amann, H.: Coagulation-fragmentation processes. Arch. Rat. Mech. Anal. 151, 339-366 (2000)
3. Baranger, C: Collisions, coalescences et fragmentations des gouttelettes dans un spray: écriture précise des équations relatives au modèle TAB. Mémoire de DEA, ENS de Cachan, 2001
4. Bardos, C., Degond, P.: Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data. Ann. Inst. H. Poincaré Anal. Non Linéaire 2, 101-118 (1985)
5. Bénilan, Ph., Wrzosek, D.: On an infinite system of reaction-diffusion equations. Adv. Math. Sci. Appl. 7, 349-364 (1997)
6. Bobylev, A.V., Illner, R.: Collision integrals for attractive potentials. J. Statist. Phys. 95, 633-649 (1999)
7. Bouchut, F., Golse, F., Pulvirenti, M.: Kinetic equations and asymptotic theory. Series in Appl. Math. Paris: Gauthiers-Villars, 2000
8. Bouchut, F., James, F.: Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness. Comm. Partial Differ. Eq. 24, 2173-2189 (1999)
9. Brenier, Y., Grenier, E.: Sticky particles and scalar conservation laws. SIAM J. Numer. Anal. 35, 2317-2328 (1998)
10. Brazier-Smith, P.R., Jennings, S.G., Latham, J.: The interaction of falling water drops: Coalescence. Proc. R. Soc. London 326, 393-408 (1972)
11. Collet, J.F., Poupaud, F.: Existence of solutions to coagulation- fragmentation systems with diffusion. Transport Theory Statist. Phys. 25, 503-513 (1996)
12. Davies, M.H., Sartor, I.D.: Theoretical collision efficiencies for small cloud droplets in Stokes flow. Nature 215, 1371-1372 (1967)
13. Deaconu, M., Fournier, N.: Probabilistic approach of some discrete and continuous coagulation equations with diffusion. Stochastic Process. Appl. 101, 83-111 (2002)
14. Dellacherie, C., Meyer, P.A.: Probabilités et potentiel, chapitres I à IV. Paris: Hermann, 1975
15. DiPerna, R.J., Lions, P.-L.: On the Cauchy problem for Boltzmann equations: Global existence and stability. Ann. Math. 130, 321-366 (1989)
16. DiPerna, R.J., Lions, P.-L.: Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98, 511-547 (1989)
17. DiPerna, R.J., Lions, P.-L.: Global solutions of Boltzmann's equation and the entropy inequality. Arch. Rat. Mech. Anal. 114, 47-55 (1991)
18. p regularity of velocity averages. Ann. Inst. H. Poincaré Anal. Non Linéaire 8, 271-287 (1991)
19. Drake, R.L.: A general mathematical survey of the coagulation equation. In Topics in Current Aerosol Research (part 2) International Reviews in Aerosol Physics and Chemistry, Oxford: Pergamon Press, 1972, pp. 203-376
20. Dubovskii, P.B.: Mathematical Theory of Coagulation. Lecture Notes Series 23, Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul, 1994
21. Dufour, G., Massot, M., Villedieu, Ph.: Etude d'un modèle de fragmentation secondaire pour les brouillards de gouttelettes. C. R. Math. Acad. Sci. Paris 336, 447-452 (2003)
22. Escobedo, M., Mischler, S., Perthame, B.: Gelation in coagulation and fragmentation models. Commun. Math. Phys. 231(1), 157-188 (2002)
23. Fournier, N., Mischler, S.: A Boltzmann equation for elastic, inelastic and coalescing collisions. Submitted
24. Friedlander, S. K.: Smoke, Dust and Haze. Reading, MA: Addison-Wesley Publishing Company, 1977
25. Illner, R.: Stellar dynamics and plasma physics with corrected potentials: Vlasov, Manev, Boltzmann, Smoluchowski. In: Hydrodynamic limits and related topics (Toronto, ON, 1998), Fields Inst. Commun. 27, Providence, RI: Am. Math. Soc., 2000, pp. 95-108
26. Jabin, P.E., Soler, J.: A Kinetic Description of Particle Fragmentations. Preprint, 2002
27. Langmuir, I.: The production of rain by a chain reaction in cumulus clouds at temperature above freezing. J. Meteor. 5, 175-192 (1948)
28. 1. Rev. Mat. Iberoamericana 18, 221-235 (2002)
29. Laurençot, Ph., Mischler, S.: The continuous coagulation- fragmentation equations with diffusion. Arch. Rat. Mech. Anal. 162, 45-99 (2002)
30. ème cycle, Université de Paris VI, 1977
31. Lions, P.-L., Perthame, B., Tadmor, E.: A kinetic formulation of multidimensional scalar conservation laws and related equations. J. Am. Math. Soc. 7, 169-191 (1994)
32. Melzak, Z.A.: A scalar transport equation. Trans. Am. Math. Soc. 85, 547-560 (1957)
33. Mischler, S., Rodriguez Ricard, M.: Existence globale pour l'équation de Smoluchowski continue non homogène et comportement asymptotique des solutions. C. R. Math. Acad. Sci. Paris 336, 407-412 (2003)
34. Perthame, B.: Time decay, propagation of low moments and dispersive effects for kinetic equations. Comm. Partial Differential Equations 21, 659-686 (1996)
35. Rao, M.M., Ren, Z.D.: Theory of Orlicz Spaces. Monogr. Textbooks Pure Appl. Math. 146, New York: Marcel Dekker, Inc., 1991
36. O'Rourke, P.J.: Collective drop effects on vaporizing liquid sprays. Ph.D. Thesis, Los Alamos National Laboratory, Los Alamos, NM 87545, November 1981
37. Roquejoffre, J.M., Villedieu, Ph.: A kinetic model for droplet coalescence in dense sprays. Math. Models Methods Appl. Sci. 11, 867-882 (2001)
38. Villedieu, Ph., Hylkema, J.: Une méthode particulaire aléatoire reposant sur une équation cinétique pour la simulation numérique des sprays denses de gouttelettes liquides. C. R. Acad. Sci. Paris Sér. I Math. 325, 323-328 (1997)
39. Williams, F.A.: Combustion Theory. Reading, MA: Addison-Wesley Publishing Company, 1985
40. Zeldovich, Ya.B.: Gravitational instability: An approximate theory for large density perturbations. Astron. Astrophys. 5, 84-89 (1970)