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Hydrodynamic limit of coagulationfragmentation type models of knary interacting particles
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Kolokoltsov, V. N. (Vasiliĭ Nikitich). (2004) Hydrodynamic limit of coagulationfragmentation type models of knary interacting particles. Journal of Statistical Physics, Vol.115 (No.5/6). pp. 16211653. ISSN 00224715

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Official URL: http://dx.doi.org/10.1023/B:JOSS.0000028071.96950....
Abstract
Hydrodynamic limit of general knary mass exchange processes with discrete mass distribution is described by a system of kinetic equations that generalize classical Smoluchovski's coagulation equations and many other models that are intensively studied in the current mathematical and physical literature. Existence and uniqueness theorems for these equations are proved. At last, for knary mass exchange processes with k > 2 an alternative nondeterministic measurevalued limit (diffusion approximation) is discussed.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Statistics 
Library of Congress Subject Headings (LCSH):  Particles  Dynamics, Particles  Mathematical models, Mass transfer  Mathematical models 
Journal or Publication Title:  Journal of Statistical Physics 
Publisher:  Springer 
ISSN:  00224715 
Date:  2004 
Volume:  Vol.115 
Number:  No.5/6 
Page Range:  pp. 16211653 
Identification Number:  10.1023/B:JOSS.0000028071.96950.12 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
References:  [Al] D.J. Aldous. Deterministic and stochastic models for coalescence (aggregation and coagulation): a review of the meanfield theory for probabilists. Bernoulli 5:2 (1999), 348. [Am] H. Amann. CoagulationFragmentation processes. Arch. Rational Mech. Anal. 151 (2000), 339366. [BC] J.M. Ball, J. Carr. The discrete coagulationfragmentation equations: existence, uniqueness and density conservation. J. Stat. Phys. 61 (1990), 203234. [Be] V.P. Belavkin. Quantum branching processes and nonlinear dynamics of multi quantum systems. Dokl. Acad. Nauk SSSR 301:6 (1988), 13481352. Engl. Tansl. in Sov. Phys. Dokl. 33:8 (1988), 581582. [BK] V. Belavkin, V. Kolokoltsov. On general kinetic equation for many particle systems with interaction, fragmentation and coagulation. Proc. R. Soc. Lond. A 459 (2002), 122. [BW] Ph. Benian, D. Wrzosek. On infinite system of reactiondiffusion equations. Adv. Math. Sci. Appl. 7 (1997), 349364. [Br1] J. Bertoin. Homogeneous fragmentation processes. Prob. Theory Relat. Fields 121 (2001), 301318. [Br2] J. Bertoin. Selfsimilar fragmentations. Ann. Inst. H. Poincare Probab. Stat. 38 (2002), 319340. [BL] J. Bertoin, J.F. LeGall. Stochastic flows associated to coalescent processes. Preprint 2002 Available via http://felix.proba.jussieu.fr/mathdoc/preprints/ [CC] J. Carr, F. da Costa. Instantaneous gelation in coagulation dynamics. Z. Angew. Math. Phys. 43 (1992), 974983. [CP] J.F. Collet, F. Poupaud. Existence of solutions to coagulationfragmentation systems with diffusion. Transport Theory Statist. Phys. 25 (1996), 503513. [Da] D. Dawson. MeasureValued Markov Processes. Hennequin P.L. (ed.) Ecole d'Ete de probabilit¶es de SaintFlour XXI1991. Springer Lect. Notes Math. 1541 (1993), 1260. [DKW] S.C. Davies, J.R. King and J.A. Wattis. The Smoluchovski coagulation equations with continuous injection. J. Phys. A: Math. Gen. 32 (1999), 77457763. [Du] P.B. Dubovski. A "triangle" of interconnected coagulation models. J. Phys. A: Math.Gen. 32 (1999), 781793. [Dy] E. Dynkin. An Introduction to Branching MeasureValued Processes. CRM monograph series 6, AMS, Providence RI, 1994. [EK] S.N. Ethier, T.G. Kurtz. Markov Processes. Characterization and convergence. John Wiley Sons 1986. [Ja] N. Jacob. Pseudodifferential operators and Markov processes. Vol. II: Generators and their potential theory. London: Imperial College Press, 2002. [Je] I. Jeon. Existence of Gelling Solutions for CoagulationFragmentation Equations. Comm. Math. Phys. 194 (1998), 541567. [Ko1] V. Kolokoltsov. Measurevalued limits of interacting particle systems with knary interactions I. Onedimensional limits. Probab. Theory Relat. Fields 126 (2003), 364394. [Ko2] V. Kolokoltsov. Measurevalued limits of interacting particle systems with knary interactions II. Preprint (2002). To appear in Stochastics and Stochastics Reports. [Ko3] V. Kolokoltsov. On Extensions of Mollified Boltzmann and Smoluchovski Equations to Particle Systems with a knary Interaction. Russian Journal Math. Phys. 10:3 (2003), 268295. [Ko4] V. Kolokoltsov. Symmetric stable laws and stablelike jumpdiffusions. Proc. London Math. Soc. 3:80 (2000), 725768. [Ko5] V. Kolokoltsov. On Markov processes with decomposable pseudodifferential generators. Preprint (2002). To appear in Stochastics and Stochastics Reports. [KK] M. Kostoglou, A.J. Karabelas. A study of nonlinear breakage equation: Analytical and asymptotic solutions. J. Phys. A: Math.Gen. 33 (2000), 12211232. [LLW] M. Lachowicz, Ph. Laurencot, D. Wrzosek. On the OortHulstSavronov coagulation equation and its relation to the Smoluchowski equation. SIAM J. Math. Anal. 34 (2003), 13991421. [LM] Ph. Laurencot, S. Mischler. The Continuous CoagulationFragmentation Equations with Diffusion. Arch. Rational Mech. Anal. 162 (2002), 4599. [LW] P. Laurencot, D. Wrzosek. The Discrete Coagulation Equations with Collisional Breakage. J. Stat. Phys. 104, 1/2 (2001), 193220. [MS] M. MÄohle, S. Sagitov. A classification of coalescent processes for haploid exchangeable population models. Ann. Prob. 29 (2001), 15471562. [No1] J. Norris. Smoluchovski's Coagulation Equation: Uniqueness, Nonuniqueness and a Hydrodynamic Limit for the Stochastic Coalescent. The Annals of Applied Probability 9:1 (1999), 78109. [No2] J. Norris. Cluster Coagulation. Comm. Math. Phys. 209 (2000), 407435. [Ok] A. Okubo. Dynamical aspects of animal grouping: swarms, schools, flocks and herds. Adv. Biophys 22 (1986), 194. [Pi] J.Pitman. Coalescents with multiple collisions. Ann. Prob. 27 (1999), 18701902. [Sa] V.S. Safronov. Evolution of the PrePlanetary Cloud and the Formation of the Earth and Planets. Moscow, Nauka, 1969 (in Russian). Engl. transl.: Israel Program for Scientific Translations, Jerusalem, 1972. [Sc] J. Schweinsberg. Coalescents with simultaneous multiple collisions. Electr. J. Prob. 5 (2000), 150. [Sr] R.C. Srivastava. A simple model of particle coalescence and breaup. J. Atmos. Sci. 39 (1982), 13171322. [Sz] A. Sznitman. Topics in Propagation of Chaos. In: Ecole d'Ete de Probabilites de SaintFlour XIX1989. Springer Lecture Notes Math. 1464 (1991), 167255. [Wi] D. Wilkins. A geometrical interpretation of the coagulation equation. J. Phys. A: Math. Gen. 15 (1982), 11751178. [Wr] D. Wrzosek. Massconservation solutions to the discrete coagulationfragmentation model with diffusion. Nonlinear Anal. 49 (2002), 297314. 
URI:  http://wrap.warwick.ac.uk/id/eprint/39383 
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