Liapunov functionals for smoluchowski's coagulation equation and convergence to self-similarity

Monatshefte fur Mathematik

Volumn 146, Issue 2, 2005, Pages 127-142

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

^a UNIVERSITÉ DE TOULOUSE   (France)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

^c CNRS   (France)

Author keywords

Coagulation; Liapunov functional; Self similar solution

Indexed keywords

EID: 26044453611     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00605-005-0308-1     Document Type: Article

References (24)

1. Aizenman M, Bak TA (1979) Convergence to equilibrium in a system of reacting polymers. Comm Math Phys 65: 203-230
2. Aldous DJ (1999) Deterministic and stochastic models for coalescence (aggregation, coagulation): a review of the mean-field theory for probabilists. Bernoulli 5: 3-48
3. Bertoin J (2002) Eternal solutions to Smoluchowski's coagulation equation with additive kernel and their probabilistic interpretations, Ann Appl Probab 12: 547-564
4. da Costa FP (1996) On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations. Proc Edinburgh Math Soc (2) 39: 547-559
5. Deaconu M, Tanré E (2000) Smoluchowski's coagulation equation: probabilistic interpretation of solutions for constant, additive and multiplicative kernels, Ann Scuola Norm Sup Pisa Cl Sci (4) 29: 549-579
6. van Dongen PGJ, Ernst MH (1988) Scaling solutions of Smoluchowski's coagulation equation, J Statist Phys 50: 295-329
7. Drake RL (1972) A general mathematical survey of the coagulation equation. In: Topics in Current Aerosol Research (part 2), pp 203-376. International Reviews in Aerosol Physics and Chemistry, Oxford: Pergamon Press
8. Escobedo M, Laurençot Ph, Mischler S, Perthame B (2003) Gelation and mass conservation in coagulation-fragmentation models. J Differential Equations 195: 143-174
9. Escobedo M, Mischler S, Rodriguez Ricard M (2005) On self-similarity and stationary problem for fragmentation and coagulation models. Ann Institut Henri Poincaré - Analyse non linéaire 22: 99-125
10. Filbet F, Laurençot Ph (2004) Numerical simulation of the Smoluchowski coagulation equation. SIAM J Sci Comput 25: 2004-2028
11. Fournier N, Laurençot Ph (2005) Existence of self-similar solutions to Smoluchowski's coagulation equation. Comm Math Phys (in press)
12. Friedlander SK, Wang CS (1966) The self-preserving particle size distribution for coagulation by brownian motion. J Colloid Interface Sci 22: 126-132
13. Kreer M, Penrose O (1994) Proof of dynamical scaling in Smoluchowski's coagulation equation with constant kernel. J Statist Phys 75: 389-407
14. Krivitsky DS (1995) Numerical solution of the Smoluchowski kinetic equation and asymptotics of the distribution function, J Phys A 28: 2025-2039
15. Laurençot Ph, Mischler S (2002) The continuous coagulation-fragmentation equation with diffusion. Arch Rational Mech Anal 162: 45-99
16. Laurençot Ph, Mischler S (2003) Convergence to equilibrium for the continuous coagulation-fragmentation equation. Bull Sci Math 127: 179-190
17. Laurençot Ph, Mischler S (2004) On coalescence equations and related models. In: Degond P, Pareschi L, Russo G (eds) Modeling and Computational Methods for Kinetic Equations, pp 321-356, Boston: Birkhäuser
18. Lee MH (2002) A survey of numerical solutions to the coagulation equation. J Phys A 34: 10219-10241
19. Leyvraz F (2003) Scaling theory and exactly solved models in the kinetics of irreversible aggregation. Phys Rep 383: 95-212
20. Meesters A, Ernst MH (1987) Numerical evaluation of self-preserving spectra in Smoluchowski's coagulation theory. J Colloid Interface Sci 119: 576-587
21. Menon G. Pego RL (2003) Dynamical scaling in Smoluchowski's coagulation equations: uniform convergence. Preprint
22. Menon G, Pego RL (2004) Approach to self-similarity in Smoluchowski's coagulation equations. Comm Pure Appl Math 57: 1197-1232
23. Smoluchowski M (1916) Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen. Physik Zeitschr 17: 557-599
24. Smoluchowski M (1917) Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen. Z phys Chem 92: 129-168