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Volumn 2, Issue , 2004, Pages 35-54

SOME MODELLING ISSUES IN THE THEORY OF FRAGMENTATION-COAGULATION SYSTEMS*

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EID: 33749483400     PISSN: 15396746     EISSN: 19450796     Source Type: Journal    
DOI: 10.4310/CMS.2004.v2.n5.a3     Document Type: Article
Times cited : (32)

References (37)
  • 1
    • 0001796185 scopus 로고    scopus 로고
    • Deterministic and stochastic models for coalescence (aggregation, coagulation): a review of the mean-field theory for probabilists
    • [1]
    • [1] D. Aldous, Deterministic and stochastic models for coalescence (aggregation, coagulation): a review of the mean-field theory for probabilists, Bernoulli, 5:3-48, 1999.
    • (1999) Bernoulli , vol.5 , pp. 3-48
    • Aldous, D.1
  • 2
    • 0036330936 scopus 로고    scopus 로고
    • Eternal solutions to Smoluchowski,s coagulation equation with additive kernel and their probabilistic interpretations
    • [2]
    • [2] J. Bertoin, Eternal solutions to Smoluchowski,s coagulation equation with additive kernel and their probabilistic interpretations, Ann. Appl. Probab., 12(2):547-564, 2002.
    • (2002) Ann. Appl. Probab , vol.12 , Issue.2 , pp. 547-564
    • Bertoin, J.1
  • 3
    • 0000262385 scopus 로고
    • On the asymptotic behavior of generalized processes, with applications to nonlinear evolution equations
    • [3]
    • [3] J.M. Ball, On the asymptotic behavior of generalized processes, with applications to nonlinear evolution equations, J. Differential Equations, 27(2):224-265, 1978.
    • (1978) J. Differential Equations , vol.27 , Issue.2 , pp. 224-265
    • Ball, J.M.1
  • 4
    • 0003222693 scopus 로고
    • On the theory of generalized dynamical systems
    • [4]
    • [4] E.A. Barbashin, On the theory of generalized dynamical systems, Moskov. Gos. Ped. Inst. Ucen.Zap., 2:110-133, 1948.
    • (1948) Moskov. Gos. Ped. Inst. Ucen.Zap , vol.2 , pp. 110-133
    • Barbashin, E.A.1
  • 5
    • 0000120890 scopus 로고
    • The Becker-Doring cluster equations: Basic properties and asymptotic behaviour of solutions
    • [5]
    • [5] J.M. Ball, J. Carr, and O. Penrose, The Becker-Doring cluster equations: Basic properties and asymptotic behaviour of solutions, Comm. Math. Phys., 104:657-692, 1986.
    • (1986) Comm. Math. Phys , vol.104 , pp. 657-692
    • Ball, J.M.1    Carr, J.2    Penrose, O.3
  • 6
    • 84934935637 scopus 로고
    • Kinetische behandlung der keimbildung in ubersattigten damfern
    • [6]
    • [6] R. Becker and W. Doring, Kinetische behandlung der keimbildung in ubersattigten damfern, Ann. Phys., (Leipzig) 24:719-752, 1935.
    • (1935) Ann. Phys., (Leipzig) , vol.24 , pp. 719-752
    • Becker, R.1    Doring, W.2
  • 7
    • 84990739185 scopus 로고
    • Renormalization group and asymptotics of solutions of nonlinear parabolic equations
    • [7]
    • [7] J. Bricmont, A. Kupiainen, and G. Lin, Renormalization group and asymptotics of solutions of nonlinear parabolic equations, Comm. Pure Appl. Math., 47(6):893-922, 1994.
    • (1994) Comm. Pure Appl. Math , vol.47 , Issue.6 , pp. 893-922
    • Bricmont, J.1    Kupiainen, A.2    Lin, G.3
  • 9
    • 0001540136 scopus 로고    scopus 로고
    • Asymptotic behaviour of solutions to a simplified Lifshitz-Slyozov equa-tion
    • [9]
    • [9] J. Carr and O. Penrose, Asymptotic behaviour of solutions to a simplified Lifshitz-Slyozov equa-tion, Phys., D 124(1-3):166-176, 1998.
    • (1998) Phys., D , vol.124 , Issue.1-3 , pp. 166-176
    • Carr, J.1    Penrose, O.2
  • 10
    • 0036258644 scopus 로고    scopus 로고
    • Decay of monomer concentration in the Lifshitz-Slyozov equation
    • [10]
    • [10] J.F. Collet, T. Goudon, and A. Vasseur, Decay of monomer concentration in the Lifshitz-Slyozov equation, J. Stat. Phys., 108(1):341-359, 2002.
    • (2002) J. Stat. Phys , vol.108 , Issue.1 , pp. 341-359
    • Collet, J.F.1    Goudon, T.2    Vasseur, A.3
  • 11
    • 0012548294 scopus 로고    scopus 로고
    • Smoluchowski,s coagulation equation: probabilistic interpretation of solutions for constant, additive and multiplicative kernels
    • [11]
    • [11] M. Deaconu and E. Tanr6, Smoluchowski,s coagulation equation: probabilistic interpretation of solutions for constant, additive and multiplicative kernels, Ann. Sc. Norm. Pisa Cl. Sci., XXIX(4):549-579, 2000.
    • (2000) Ann. Sc. Norm. Pisa Cl. Sci , vol.XXIX , Issue.4 , pp. 549-579
    • Deaconu, M.1    Tanr6, E.2
  • 12
    • 0002350128 scopus 로고    scopus 로고
    • A modified version of the Lifshitz-Slyozov model
    • [12]
    • [12] S. Hariz and J.F. Collet, A modified version of the Lifshitz-Slyozov model, Letters in Applied Mathematics, 12:81-85, 1999.
    • (1999) Letters in Applied Mathematics , vol.12 , pp. 81-85
    • Hariz, S.1    Collet, J.F.2
  • 13
    • 85128843703 scopus 로고    scopus 로고
    • Quelques exemples de transitions de phase du premier ordre: les modelesd,aglomeration
    • [13]
    • [13] J.F. Collet, Quelques exemples de transitions de phase du premier ordre: les modelesd,aglomeration, Matapli, 64:29-39, 2001.
    • (2001) Matapli , vol.64 , pp. 29-39
    • Collet, J.F.1
  • 14
    • 0036588843 scopus 로고    scopus 로고
    • The Becker-Doring model and its Lifshitz-Slyozov asymptotics
    • [14]
    • [14] J.F. Collet, T. Goudon, F. Poupaud, and A. Vasseur, The Becker-Doring model and its Lifshitz-Slyozov asymptotics, SIAM J. Appl. Math., 62(5):1488-1500, 2002.
    • (2002) SIAM J. Appl. Math , vol.62 , Issue.5 , pp. 1488-1500
    • Collet, J.F.1    Goudon, T.2    Poupaud, F.3    Vasseur, A.4
  • 18
    • 0000391826 scopus 로고
    • Gel, self-similarity and universality in the discrete Smoluchowski equation with finite mass
    • [18]
    • [18] Y. Gabellini and J.L. Meunier, Gel, self-similarity and universality in the discrete Smoluchowski equation with finite mass, J. Phys. A, Math. Gen., 25(13):3683-3700, 1992.
    • (1992) J. Phys. A, Math. Gen , vol.25 , Issue.13 , pp. 3683-3700
    • Gabellini, Y.1    Meunier, J.L.2
  • 20
    • 0003460899 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • [20] Springer-Verlag, Berlin-New York
    • [20] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics,840. Springer-Verlag, Berlin-New York, 1981.
    • (1981) Lecture Notes in Mathematics , vol.840
    • Henry, D.1
  • 21
    • 0004256690 scopus 로고
    • [21] Academic Press
    • [21] G.M. Hidy, Aerosols, Academic Press, 1984.
    • (1984) Aerosols
    • Hidy, G.M.1
  • 22
    • 0038346787 scopus 로고    scopus 로고
    • On the rate of convergence to equilibrium in the Becker-Dooring equations
    • [22]
    • [22] PE. Jabin and B. Niethammer, On the rate of convergence to equilibrium in the Becker-Dooring equations, J. Diff. Eq., 191(2):518-543, 2003.
    • (2003) J. Diff. Eq , vol.191 , Issue.2 , pp. 518-543
    • Jabin, PE.1    Niethammer, B.2
  • 24
    • 22044455391 scopus 로고    scopus 로고
    • Kinetics of first-order phase transitions in the asymptotic stage
    • [24]
    • [24] S.A. Kukushkin and A.V. Osipov, Kinetics of first-order phase transitions in the asymptotic stage, J. Exp. Theor. Phys., 86(6):1201-1208, 1998.
    • (1998) J. Exp. Theor. Phys , vol.86 , Issue.6 , pp. 1201-1208
    • Kukushkin, S.A.1    Osipov, A.V.2
  • 26
    • 33646109512 scopus 로고
    • The kinetics of precipitation from supersaturated solid solutions
    • [26]
    • [26] I.M. Lifshitz and V.V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. of Phys. and Chem. of Solids, 19:35-50, 1961.
    • (1961) J. of Phys. and Chem. of Solids , vol.19 , pp. 35-50
    • Lifshitz, I.M.1    Slyozov, V.V.2
  • 28
    • 0035538503 scopus 로고    scopus 로고
    • The LSW model for domain coarsening: asymptotic behavior forconserved total mass
    • [28]
    • [28] B. Niethammer, R.L. Pego, The LSW model for domain coarsening: asymptotic behavior forconserved total mass, J. Statist. Phys., 104(5-6):1113-1144, 2001.
    • (2001) J. Statist. Phys , vol.104 , Issue.5-6 , pp. 1113-1144
    • Niethammer, B.1    Pego, R.L.2
  • 30
    • 0001138912 scopus 로고
    • Drei vortr&ge uber diffusion, brownsche bewegung und koagulation von kolloidteilchen
    • [30]
    • [30] M.V. Smoluchowski, Drei vortr&ge uber diffusion, brownsche bewegung und koagulation von kolloidteilchen, Phys. Z., 17:557-585, 1916.
    • (1916) Phys. Z , vol.17 , pp. 557-585
    • Smoluchowski, M.V.1
  • 31
    • 0000267310 scopus 로고
    • Versus einer mathematischen theorie der kolloιden losungen
    • [31]
    • [31] M.V. Smoluchowski, Versus einer mathematischen theorie der kolloιden losungen, Z. Phys.Chem., 92:129-168, 1917.
    • (1917) Z. Phys.Chem , vol.92 , pp. 129-168
    • Smoluchowski, M.V.1
  • 32
    • 0032632377 scopus 로고    scopus 로고
    • Entropy production and the rate of convergence to equilibrium for the Fokker-Planck equation
    • [32]
    • [32] G. Toscani, Entropy production and the rate of convergence to equilibrium for the Fokker-Planck equation, Quart. Appl. Math., 57(3):521-541, 1999.
    • (1999) Quart. Appl. Math , vol.57 , Issue.3 , pp. 521-541
    • Toscani, G.1
  • 33
    • 84956073446 scopus 로고    scopus 로고
    • Diffusive decomposition of solid solutions
    • [33]
    • [33] V.V, Slyozov and V.V. Sagalovich, Diffusive decomposition of solid solutions, Sov. Phys. Usp.,30(1):23-45, 1997.
    • (1997) Sov. Phys. Usp , vol.30 , Issue.1 , pp. 23-45
    • Slyozov, V.V1    Sagalovich, V.V.2
  • 34
    • 33747627898 scopus 로고
    • Scaling solutions of Smoluchowski,s coagulation equation
    • [34]
    • [34] P.G.J. Van Dongen and M.H. Ernst, Scaling solutions of Smoluchowski,s coagulation equation,J. Statist. Phys., 50(1-2), 1988.
    • (1988) J. Statist. Phys , vol.50 , Issue.1-2
    • Van Dongen, P.G.J.1    Ernst, M.H.2
  • 35
    • 0040040086 scopus 로고    scopus 로고
    • The Becker-Doring equations and the Lifshitz-Slyozov theory of coarsening
    • [35]
    • [35] J.J.L. Velazquez, The Becker-Doring equations and the Lifshitz-Slyozov theory of coarsening,J. Statist. Phys., 92(1-2):195-236, 1998.
    • (1998) J. Statist. Phys , vol.92 , Issue.1-2 , pp. 195-236
    • Velazquez, J.J.L.1
  • 36
    • 2442557820 scopus 로고    scopus 로고
    • Topics in optimal transportation
    • [36] American Mathematical Society
    • [36] C. Villani, Topics in optimal transportation, Graduate Studies in Mathematics, 58. American Mathematical Society.
    • Graduate Studies in Mathematics , vol.58
    • Villani, C.1
  • 37
    • 0001333772 scopus 로고
    • Theorie der alterung von niederschl&gen durch umlosen
    • [37]
    • [37] C. Wagner, Theorie der alterung von niederschl&gen durch umlosen, Z. Elektrochem. 65:581-594, 1961.
    • (1961) Z. Elektrochem , vol.65 , pp. 581-594
    • Wagner, C.1


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