Convergence to equilibrium for the continuous coagulation-fragmentation equation

Bulletin des Sciences Mathematiques

Volumn 127, Issue 3, 2003, Pages 179-190

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

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

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

^c ÉCOLE NORMALE SUPÉRIEURE   (France)

Author keywords

Convergence to equilibrium; H Theorem; LaSalle invariance principle

Indexed keywords

EID: 0038794181     PISSN: 00074497     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0007-4497(02)00002-7     Document Type: Article

References (22)

1. Aizenman M. Bak T.A. Convergence to equilibrium in a system of reacting polymers Comm. Math. Phys. 65 1979 203-230
2. Aldous D.J. Deterministic and stochastic models for coalescence (aggregation, coagulation): a review of the mean-field theory for probabilists Bernoulli 5 1999 3-48
3. Ball J.M. Carr J. Penrose O. The Becker-Döring cluster equations: basic properties and asymptotic behaviour of solutions Comm. Math. Phys. 104 1986 657-692
4. Burobin A.V. Existence and uniqueness of a solution of a Cauchy problem for the inhomogeneous three-dimensional coagulation equation Differential Equations 19 1983 1187-1197
5. Carr J. Asymptotic behaviour of solutions to the coagulation-fragmentation equations. I. The strong fragmentation case Proc. Roy. Soc. Edinburgh Sect. A 121 1992 231-244
6. Carr J. da Costa F.P. Asymptotic behavior of solutions to the coagulation-fragmentation equations. II. Weak fragmentation J. Statist. Phys. 77 1994 89-123
7. Collet J.F. Poupaud F. Asymptotic behaviour of solutions to the diffusive fragmentation-coagulation system Phys. D 114 1998 123-146
8. da Costa F.P. Convergence to equilibria of solutions to the coagulation-fragmentation equations Nonlinear Evolution Equations and Their Applications (Macau, 1998) 1999 45-56 World Sci. Publishing River Edge, NJ
9. 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 1972 203 376 Pergamon Press Oxford
10. Dubovskiǐ P.B. Stewart I.W. Existence, uniqueness and mass conservation for the coagulation-fragmentation equation Math. Methods Appl. Sci. 19 1996 571-591
11. M. Escobedo, Ph. Laurençot, S. Mischler, B. Perthame, Gelation and mass conservation in coagulation-fragmentation models, Preprint
12. Escobedo M. Mischler S. Perthame B. Gelation in coagulation and fragmentation models Comm. Math. Phys. 231 2002 157-188
13. Galkin V.A. Tupchiev V.A. About asymptotic behaviour of solutions of the coagulation equation Transactions of the Institute of Experimental Meteorology 19 1978 31-41 (in Russian)
14. Jeon I. Existence of gelling solutions for coagulation-fragmentation equations Comm. Math. Phys. 194 1998 541-567
15. Laurençot Ph. Wrzosek D. The Becker-Döring model with diffusion. II. Long-time behaviour J. Differential Equations 148 1998 268-291
16. Laurençot Ph. Mischler S. The continuous coagulation-fragmentation equation with diffusion Arch. Rational Mech. Anal. 162 2002 45-99
17. Laurençot Ph. Mischler S. From the discrete to the continuous coagulation-fragmentation equations Proc. Roy. Soc. Edinburgh Sect. A 132 2002 1219-1248
18. ème cycle, Université de Paris VI 1977
19. Lions P.-L. Compactness in Boltzmann's equation via Fourier integral operators and applications I J. Math. Kyoto Univ. 34 1994 391-427
20. Lu X.G. Conservation of energy, entropy identity and local stability for the spatially homogeneous Boltzmann equation J. Statist. Phys. 96 1999 765-796
21. Slemrod M. The Becker-Döring equations Modeling in Applied Sciences, Model. Simul. Sci. Eng. Technol. 2000 149-171 Birkhäuser Boston Boston, MA
22. Stewart I.W. Dubovskii P.B. Approach to equilibrium for the coagulation-fragmentation equation via a Lyapunov functional Math. Methods Appl. Sci. 19 1996 171-185