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Volumn 115, Issue 5-6, 2004, Pages 1621-1653

Hydrodynamic limit of coagulation-fragmentation type models of k-nary interacting particles

Author keywords

Coagulation fragmentation; Diffusion approximation; Interacting particles; k nary interaction; Kinetic equation; Mass exchange processes; Measure valued limits

Indexed keywords


EID: 3543019744     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:joss.0000028071.96950.12     Document Type: Article
Times cited : (12)

References (39)
  • 1
    • 0001796185 scopus 로고    scopus 로고
    • Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists
    • D. J. Aldous, Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists, Bernoulli 5:3-48 (1999).
    • (1999) Bernoulli , vol.5 , pp. 3-48
    • Aldous, D.J.1
  • 2
    • 0034405834 scopus 로고    scopus 로고
    • Coagulation-fragmentation processes
    • H. Amann, Coagulation-fragmentation processes, Arch. Rational Mech. Anal. 151: 339-366 (2000).
    • (2000) Arch. Rational Mech. Anal. , vol.151 , pp. 339-366
    • Amann, H.1
  • 3
    • 0001236857 scopus 로고
    • The discrete coagulation-fragmentation equations: Existence, uniqueness, and density conservation
    • J. M. Ball and J. Carr, The discrete coagulation-fragmentation equations: Existence, uniqueness, and density conservation, J. Stat. Phys. 61:203-234 (1990).
    • (1990) J. Stat. Phys. , vol.61 , pp. 203-234
    • Ball, J.M.1    Carr, J.2
  • 4
    • 0043243580 scopus 로고
    • Quantum branching processes and nonlinear dynamics of multi-quantum systems
    • V. P. Belavkin, Quantum branching processes and nonlinear dynamics of multi-quantum systems, Dokl. Acad. Nauk SSSR 301:1348-1352 (1988). Engl. Transl. in Sov. Phys. Dokl. 33:581-582 (1988).
    • (1988) Dokl. Acad. Nauk SSSR , vol.301 , pp. 1348-1352
    • Belavkin, V.P.1
  • 5
    • 0042742391 scopus 로고
    • Engl. Transl.
    • V. P. Belavkin, Quantum branching processes and nonlinear dynamics of multi-quantum systems, Dokl. Acad. Nauk SSSR 301:1348-1352 (1988). Engl. Transl. in Sov. Phys. Dokl. 33:581-582 (1988).
    • (1988) Sov. Phys. Dokl. , vol.33 , pp. 581-582
  • 6
    • 0043243576 scopus 로고    scopus 로고
    • On general kinetic equation for many particle systems with interaction, fragmentation, and coagulation
    • V. Belavkin and V. Kolokoltsov, On general kinetic equation for many particle systems with interaction, fragmentation, and coagulation, Proc. Roy. Soc. London Ser. A 459:1-22 (2002).
    • (2002) Proc. Roy. Soc. London Ser. A , vol.459 , pp. 1-22
    • Belavkin, V.1    Kolokoltsov, V.2
  • 7
    • 0000459844 scopus 로고    scopus 로고
    • On infinite system of reaction-diffusion equations
    • Ph. Benian and D. Wrzosek, On infinite system of reaction-diffusion equations, Adv. Math. Sci. Appl. 7:349-364 (1997).
    • (1997) Adv. Math. Sci. Appl. , vol.7 , pp. 349-364
    • Benian, Ph.1    Wrzosek, D.2
  • 8
    • 0035621332 scopus 로고    scopus 로고
    • Homogeneous fragmentation processes
    • J. Bertoin, Homogeneous fragmentation processes, Probab. Theory Related Fields 121: 301-318 (2001).
    • (2001) Probab. Theory Related Fields , vol.121 , pp. 301-318
    • Bertoin, J.1
  • 11
    • 0001006839 scopus 로고
    • Instantaneous gelation in coagulation dynamics
    • J. Carr and F. da Costa, Instantaneous gelation in coagulation dynamics, Z. Angew. Math. Phys. 43:974-983 (1992).
    • (1992) Z. Angew. Math. Phys. , vol.43 , pp. 974-983
    • Carr, J.1    Da Costa, F.2
  • 12
    • 0030503865 scopus 로고    scopus 로고
    • Existence of solutions to coagulation-fragmentation systems with diffusion
    • J. F. Collet and F. Poupaud, Existence of solutions to coagulation-fragmentation systems with diffusion, Transport Theory Statist. Phys. 25:503-513 (1996).
    • (1996) Transport Theory Statist. Phys. , vol.25 , pp. 503-513
    • Collet, J.F.1    Poupaud, F.2
  • 13
    • 0002275662 scopus 로고
    • Measure-valued Markov processe
    • P. L. Hennequin, ed., Springer Lect. Notes Math., (Springer)
    • D. Dawson, Measure-valued Markov processes, in École d'été de probabilités de Saint-Flour XXI-1991, P. L. Hennequin, ed., Springer Lect. Notes Math., Vol. 1541 (Springer, 1993), pp. 1-260.
    • (1993) École d'Été de Probabilités de Saint-Flour XXI-1991 , vol.1541 , pp. 1-260
    • Dawson, D.1
  • 14
    • 0033527513 scopus 로고    scopus 로고
    • The Smoluchovski coagulation equations with continuous injection
    • S. C. Davies, J. R. King, and J. A. Wattis, The Smoluchovski coagulation equations with continuous injection, J. Phys. A: Math. Gen. 32:7745-7763 (1999).
    • (1999) J. Phys. A: Math. Gen. , vol.32 , pp. 7745-7763
    • Davies, S.C.1    King, J.R.2    Wattis, J.A.3
  • 15
    • 0033524568 scopus 로고    scopus 로고
    • A "triangle" of interconnected coagulation models
    • P. B. Dubovski, A "triangle" of interconnected coagulation models, J. Phys. A: Math. Gen. 32:781-793 (1999).
    • (1999) J. Phys. A: Math. Gen. , vol.32 , pp. 781-793
    • Dubovski, P.B.1
  • 19
    • 0032474307 scopus 로고    scopus 로고
    • Existence of gelling solutions for coagulation-fragmentation equations
    • I. Jeon, Existence of gelling solutions for coagulation-fragmentation equations, Comm. Math. Phys. 194:541-567 (1998).
    • (1998) Comm. Math. Phys. , vol.194 , pp. 541-567
    • Jeon, I.1
  • 20
    • 0041742505 scopus 로고    scopus 로고
    • Measure-valued limits of interacting particle systems with k-nary interactions I. One-dimensional limits
    • V. Kolokoltsov, Measure-valued limits of interacting particle systems with k-nary interactions I. One-dimensional limits, Probab. Theory Related Fields 126:364-394 (2003).
    • (2003) Probab. Theory Related Fields , vol.126 , pp. 364-394
    • Kolokoltsov, V.1
  • 21
    • 3543034877 scopus 로고    scopus 로고
    • Measure-valued limits of interacting particle systems with k-nary interactions II
    • Preprint, to appear
    • V. Kolokoltsov, Measure-valued limits of interacting particle systems with k-nary interactions II, Preprint (2002), to appear in Stochastics and Stochastics Reports.
    • (2002) Stochastics and Stochastics Reports
    • Kolokoltsov, V.1
  • 22
    • 0141976227 scopus 로고    scopus 로고
    • On Extensions of mollified Boltzmann and Smoluchovski equations to particle systems with a k-nary interaction
    • V. Kolokoltsov, On Extensions of mollified Boltzmann and Smoluchovski equations to particle systems with a k-nary interaction, Russian J. Math. Phys. 10:268-295 (2003).
    • (2003) Russian J. Math. Phys. , vol.10 , pp. 268-295
    • Kolokoltsov, V.1
  • 23
    • 0010003910 scopus 로고    scopus 로고
    • Symmetric stable laws and stable-like jump-diffusions
    • V. Kolokoltsov, Symmetric stable laws and stable-like jump-diffusions, Proc. London Math. Soc. 3:725-768 (2000).
    • (2000) Proc. London Math. Soc. , vol.3 , pp. 725-768
    • Kolokoltsov, V.1
  • 24
    • 3543012861 scopus 로고    scopus 로고
    • On Markov processes with decomposable pseudo-differential generators
    • Preprint, to appear
    • V. Kolokoltsov, On Markov processes with decomposable pseudo-differential generators, Preprint (2002), to appear in Stochastics and Stochastics Reports.
    • (2002) Stochastics and Stochastics Reports
    • Kolokoltsov, V.1
  • 25
    • 0034681243 scopus 로고    scopus 로고
    • A study of nonlinear breakage equation: Analytical and asymptotic solutions
    • M. Kostoglou and A. J. Karabelas, A study of nonlinear breakage equation: Analytical and asymptotic solutions, J. Phys. A: Math. Gen. 33:1221-1232 (2000).
    • (2000) J. Phys. A: Math. Gen. , vol.33 , pp. 1221-1232
    • Kostoglou, M.1    Karabelas, A.J.2
  • 26
    • 0242511215 scopus 로고    scopus 로고
    • On the Oort-Hulst-Savronov coagulation equation and its relation to the Smoluchowski equation
    • M. Lachowicz, Ph. Laurencot, and D. Wrzosek, On the Oort-Hulst-Savronov coagulation equation and its relation to the Smoluchowski equation, SIAM J. Math. Anal. 34:1399-1421 (2003).
    • (2003) SIAM J. Math. Anal. , vol.34 , pp. 1399-1421
    • Lachowicz, M.1    Laurencot, Ph.2    Wrzosek, D.3
  • 27
    • 0036004822 scopus 로고    scopus 로고
    • The continuous coagulation-fragmentation equations with diffusion
    • Ph. Laurencot and S. Mischler, The continuous coagulation-fragmentation equations with diffusion, Arch. Rational Mech. Anal. 162:45-99 (2002).
    • (2002) Arch. Rational Mech. Anal. , vol.162 , pp. 45-99
    • Laurencot, Ph.1    Mischler, S.2
  • 28
    • 0035535127 scopus 로고    scopus 로고
    • The discrete coagulation equations with collisional breakage
    • P. Laurencot and D. Wrzosek, The discrete coagulation equations with collisional breakage, J. Stat. Phys. 104:193-220 (2001).
    • (2001) J. Stat. Phys. , vol.104 , pp. 193-220
    • Laurencot, P.1    Wrzosek, D.2
  • 29
    • 0035470867 scopus 로고    scopus 로고
    • A classification of coalescent processes for haploid exchangeable population models
    • M. Möhle and S. Sagitov, A classification of coalescent processes for haploid exchangeable population models, Ann. Probab. 29:1547-1562 (2001).
    • (2001) Ann. Probab. , vol.29 , pp. 1547-1562
    • Möhle, M.1    Sagitov, S.2
  • 30
    • 0033440601 scopus 로고    scopus 로고
    • Smoluchovski's coagulation equation: Uniqueness, nonuniqueness, and a hydrodynamic limit for the stochastic coalescent
    • J. Norris, Smoluchovski's coagulation equation: Uniqueness, nonuniqueness, and a hydrodynamic limit for the stochastic coalescent, Ann. Appl. Probab. 9:78-109 (1999).
    • (1999) Ann. Appl. Probab. , vol.9 , pp. 78-109
    • Norris, J.1
  • 31
    • 0034340686 scopus 로고    scopus 로고
    • Cluster coagulation
    • J. Norris, Cluster coagulation, Comm. Math. Phys. 209:407-435 (2000).
    • (2000) Comm. Math. Phys. , vol.209 , pp. 407-435
    • Norris, J.1
  • 32
    • 0022854743 scopus 로고
    • Dynamical aspects of animal grouping: Swarms, schools, flocks, and herds
    • A. Okubo, Dynamical aspects of animal grouping: Swarms, schools, flocks, and herds, Adv. Biophys. 22:1-94 (1986).
    • (1986) Adv. Biophys. , vol.22 , pp. 1-94
    • Okubo, A.1
  • 33
    • 0033233681 scopus 로고    scopus 로고
    • Coalescents with multiple collisions
    • J. Pitman, Coalescents with multiple collisions, Ann. Probab. 27:1870-1902 (1999).
    • (1999) Ann. Probab. , vol.27 , pp. 1870-1902
    • Pitman, J.1
  • 35
    • 0001885968 scopus 로고    scopus 로고
    • Coalescents with simultaneous multiple collisions
    • J. Schweinsberg, Coalescents with simultaneous multiple collisions, Electr. J. Prob. 5:1-50 (2000).
    • (2000) Electr. J. Prob. , vol.5 , pp. 1-50
    • Schweinsberg, J.1
  • 36
    • 0020336029 scopus 로고
    • A simple model of particle coalescence and breaup
    • R. C. Srivastava, A simple model of particle coalescence and breaup, J. Atmos. Sci. 39:1317-1322 (1982).
    • (1982) J. Atmos. Sci. , vol.39 , pp. 1317-1322
    • Srivastava, R.C.1
  • 37
    • 0001105004 scopus 로고
    • Topics in propagation of chaos
    • Springer Lecture Notes Math., (Springer)
    • A. Sznitman, Topics in propagation of chaos, in École d'été de Probabilités de Saint-Flour XIX-1989, Springer Lecture Notes Math., Vol. 1464 (Springer, 1991), pp. 167-255.
    • (1991) École d'Été de Probabilités de Saint-Flour XIX-1989 , vol.1464 , pp. 167-255
    • Sznitman, A.1
  • 38
    • 0007082508 scopus 로고
    • A geometrical interpretation of the coagulation equation
    • D. Wilkins, A geometrical interpretation of the coagulation equation, J. Phys. A: Math. Gen. 15:1175-1178 (1982).
    • (1982) J. Phys. A: Math. Gen. , vol.15 , pp. 1175-1178
    • Wilkins, D.1
  • 39
    • 0036532756 scopus 로고    scopus 로고
    • Mass-conservation solutions to the discrete coagulation-fragmentation model with diffusion
    • D. Wrzosek, Mass-conservation solutions to the discrete coagulation-fragmentation model with diffusion, Nonlinear Anal. 49:297-314 (2002).
    • (2002) Nonlinear Anal. , vol.49 , pp. 297-314
    • Wrzosek, D.1


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