The continuous coagulation-fragmentation equations with diffusion

Archive for Rational Mechanics and Analysis

Volumn 162, Issue 1, 2002, Pages 45-99

  Laurençot, Philippe ^a   Mischler, Stéphane ^b,c  

^a CNRS   (France)

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

^c ÉCOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036004822     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050100186     Document Type: Article

References (43)

1. D.J. ALDOUS, Deterministic and stochastic models for coalescence (aggregation, coagulation): a review of the mean-field theory for probabilists, Bernoulli 5, (1999) 3-48.
2. M. AIZENMAN & T. A. BAK, Convergence to equilibrium in a system of reacting polymers, Comm. Math. Phys. 65, (1979) 203-230.
3. H. AMANN, Coagulation-fragmentation processes, Arch. Rational Mech. Anal. 151, (2000) 339-366.
4. P. BARAS & M. PIERRE, Problémes paraboliques semi-linéaires avec données mesures, Appl. Anal. 18, (1984) 111-149.
5. PH. BÉNILAN & D. WRZOSEK, On a infinite system of reaction-diffusion equations, Adv. Math. Sci. Appl. 7, (1997) 349-364.
6. L. BOCCARDO & T. GALLOUËT, Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal. 87, (1989) 149-169.
7. H. BREZIS, Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaees de Hilbert, North-Holland Math. Stud. 5. (North-Holland, Amsterdam 1973).
8. A.V. BUROBIN, Existence and uniqueness of a solution of a Cauchy problem for the inhomogeneous three-dimensional coagulation equation, Differential Equations 19, (1983) 1187-1197.
9. D. CHAE & P.B. DUBOVSKI, Existence and uniqueness for spatially inhomogeneous coagulation equation with sources and effluxes, Z. Angew. Math. Phys. 46, (1995) 580-594.
10. D. CHAE & P.B. DUBOVSKI, Existence and uniqueness for spatially inhomogeneous coagulation-condensation equation with unbounded kernels, J. Integral Equations Appl. 9, (1997) 219-236.
11. J. F. COLLET & F. POUPAUD, Existence of solutions to coagulation-fragmentation systems with diffusion, Transport Theory Statist. Phys. 25, (1996) 503-513.
12. J.F. COLLET & F. POUPAUD, Asymptotic behaviour of solutions to the diffusive fragmentation-coagulation system, Phys. D 114, (1998) 123-146.
13. R.J. DIPERNA & P.-L. LIONS, On the Fokker-Planck-Boltzmann equation, Comm. Math. Phys. 120, (1988) 1-23.
14. R.J. DIPERNA & P.-L. LIONS, On the Cauchy problem for Boltzmann equations: global existence and stability, Ann. Math. 130, (1989) 321-366.
15. R.J. DIPERNA & P.-L. LIONS, Global solutions of Boltzmann's equation and the entropy inequality, Arch. Rational Mech. Anal. 114, (1991) 47-55.
16. R.L. DRAKE, A general mathematical survey of the coagulation equation, in Topics in Current Aerosol Research (part 2), International Reviews in Aerosol Physics and Chemistry (Pergamon Press, Oxford 1972) 203-376.
17. P.B. DUBOVSKII, Mathematical Theory of Coagulation, Lecture Notes Series 23. (Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul 1994).
18. M.H. ERNST, R. M. ZIFF & E. M. HENDRIKS, Coagulation processes with a phase transition, J. Colloid Interface Sci. 97, (1984) 266-277.
19. M. ESCOBEDO, S. MISCHLER & B. PERTHAME, Gelation in coagulation and fragmentation models, Prépublication DMA - 01-19, ENS Paris, 2001.
20. V.A. GALKIN & V. A. TUPCHIEV, About asymptotic behaviour of solutions of the coagulation equation, Transactions of the Institute of Experimental Meteorology 19, (1978) 31-41 (in Russian).
21. F. GUIAŞ, Convergence properties of a stochastic model for coagulation-fragmentation processes with diffusion, Stochastic Anal. Appl. 19, (2001) 245-278.
22. PH. LAURENÇOT, On a class of continuous coagulation-fragmentation models, J. Differential Equations 167, (2000) 145-174.
23. 1, Rev. Mat. Iberoamericana, to appear.
24. PH. LAURENÇOT & S. MISCHLER, From the discrete to the continuous coagulation-fragmentation equations, Proc. Roy. Soc. Edinburgh Sect. A, to appear.
25. PH. LAURENÇOT & D. WRZOSEK, Fragmentation-diffusion model. Existence of solutions and asymptotic behaviour, Proc. Roy. Soc. Edinburgh Sect. A 128, (1998) 759-774.
26. PH. LAURENÇOT & D. WRZOSEK, The Becker-Döring model with diffusion. I. Basic properties of solutions, Colloq. Math. 75, (1998) 245-269.
27. PH. LAURENÇOT & D. WRZOSEK, The Becker-Döring model with diffusion. II. Long-time behaviour, J. Differential Equations 148, (1998) 268-291.
28. PH. LAURENÇOT & D. WRZOSEK, Coagulation model with partial diffusion, Z. Angew. Math. Phys. 50, (1999) 559-573.
29. ème cycle, Université de Paris VI, 1977.
30. P.-L. LIONS, Compactness in Boltzmann's equation via Fourier integral operators and applications I, J. Math. Kyoto Univ. 34, (1994) 391-427.
31. A. OKUBO, Dynamical aspects of animal grouping: swarms, schools, flocks and herds, Adv. Biophys. 22, (1986) 1-94.
32. A.S. PERELSON & R.W. SAMSEL, Kinetics of red blood cell aggregation: an example of geometric polymerization, in Kinetics of Aggregation and Gelation, F. FAMILY & D. P. LANDAU (eds.) (Elsevier, Amsterdam 1984) 137-144.
33. V.S. SAFRONOV, Evolution of the Protoplanetary Cloud and Formation of the Earth and the Planets (Israel Program for Scientific Translations Ltd., Jerusalem 1972).
34. P(O, T; B),Ann. Mat. Pura Appl. (4) 146, (1987) 65-96.
35. S. SIMONS & D. R. SIMPSON, The effect of particle coagulation on the diffusive relaxation of a spatially inhomogeneous aerosol, J. Phys. A 21, (1988) 3523-3536.
36. M. SLEMROD, Coagulation-diffusion systems: derivation and existence of solutions for the diffuse interface structure equations, Phys. D 46, (1990) 351-366.
37. M. SMOLUCHOWSKI, Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen, Physik. Zeitschr. 17, (1916) 557-599.
38. M. SMOLUCHOWSKI, Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Ltsungen, Zeitschriftf. physik. Chemic 92, (1917) 129-168.
39. I.W. STEWART, A global existence theorem for the general coagulation-fragmentation equation with unbounded kernels, Math. Methods Appl. Sci. 11, (1989) 627-648.
40. I.W. STEWART & P. B. DUBOVSKIǏ, Approach to equilibrium for the coagulation-fragmentation equation via a Lyapunov functional, Math. Methods Appl. Sci. 19, (1996) 171-185.
41. I.I. VRABIE, Compactness Methods for Nonlinear Evolutions, Second edition, Pitman Monogr. Surveys Pure Appl. Math. 75. (Longman, Harlow 1995).
42. D. WRZOSEK, Existence of solutions for the discrete coagulation-fragmentation model with diffusion, Topol. Methods Nonlinear Anal. 9, (1997) 279-296.
43. D. WRZOSEK, Mass-conserving solutions to the discrete coagulation-fragmentation model with diffusion, Nonlinear Anal. 49, (2002) 297-314.