@article{AIHPC_2006__23_3_331_0, author = {Escobedo, M. and Mischler, S.}, title = {Dust and self-similarity for the {Smoluchowski} coagulation equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {331--362}, publisher = {Elsevier}, volume = {23}, number = {3}, year = {2006}, doi = {10.1016/j.anihpc.2005.05.001}, mrnumber = {2217655}, zbl = {1154.82024}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2005.05.001/} }
TY - JOUR AU - Escobedo, M. AU - Mischler, S. TI - Dust and self-similarity for the Smoluchowski coagulation equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2006 SP - 331 EP - 362 VL - 23 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2005.05.001/ DO - 10.1016/j.anihpc.2005.05.001 LA - en ID - AIHPC_2006__23_3_331_0 ER -
%0 Journal Article %A Escobedo, M. %A Mischler, S. %T Dust and self-similarity for the Smoluchowski coagulation equation %J Annales de l'I.H.P. Analyse non linéaire %D 2006 %P 331-362 %V 23 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2005.05.001/ %R 10.1016/j.anihpc.2005.05.001 %G en %F AIHPC_2006__23_3_331_0
Escobedo, M.; Mischler, S. Dust and self-similarity for the Smoluchowski coagulation equation. Annales de l'I.H.P. Analyse non linéaire, Volume 23 (2006) no. 3, pp. 331-362. doi : 10.1016/j.anihpc.2005.05.001. http://www.numdam.org/articles/10.1016/j.anihpc.2005.05.001/
[1] Deterministic and stochastic models for coalescence (aggregation, coagulation): a review of the mean-field theory for probabilists, Bernoulli 5 (1999) 3-48. | MR | Zbl
,[2] The asymptotic behaviour of fragmentation processes, J. Eur. Math. Soc. (JEMS) 5 (4) (2003) 395-416. | MR | Zbl
,[3] Eternal solutions to Smoluchowski's coagulation equation with additive kernel and their probabilistic interpretations, Ann. Appl. Probab. 12 (2) (2002) 547-564. | MR | Zbl
,[4] Moment inequalities for the Boltzmann equation and applications to the spatially homogeneous problems, J. Statist. Phys. 88 (1997) 1183-1214. | MR | Zbl
,[5] Moment inequalities and high-energy tails for the Boltzmann equations with inelastic interactions, J. Statist. Phys. 116 (5-6) (2004) 1651-1682. | MR | Zbl
, , ,[6] Nonlinear elliptic equations with right-hand side measures, Comm. Partial Differential Equations 17 (3-4) (1992) 641-655. | MR | Zbl
, ,[7] Droplets nucleation and Smoluchovski's equation with growth and injection of particles, Phys. Rev. E 57 (1998) 881-900.
, ,[8] Cluster size distribution in irreversible aggregation at large times, J. Phys. A 18 (1985) 2779-2793. | MR
, ,[9] Solutions of Smoluchowski coagulation equation at large cluster sizes, Physica A 145 (1987) 15.
, ,[10] Scaling solutions of Smoluchowski's coagulation equation, J. Statist. Phys. 50 (1988) 295-329. | MR | Zbl
, ,[11] 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, pp. 203-376.
,[12] G. Duffa, N.T.-H. Nguyen-Bui, Un modèle de suies, Personal communication, 2002.
[13] Gelation in coagulation and fragmentation models, Comm. Math. Phys. 231 (2002) 157-188. | MR | Zbl
, , ,[14] On self-similarity and stationary problem for fragmentation and coagulation models, Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005) 99-125. | EuDML | Numdam | MR | Zbl
, , ,[15] On small particles in coagulation-fragmentation equations, J. Statist. Phys. 111 (5-6) (2003) 1299-1329. | MR | Zbl
, ,[16] N. Fournier, P. Laurençot, Existence of self-similar solutions to Smoluckovski's coagulation equation, Preprint, 2004. | MR | Zbl
[17] Smoke, Dust and Haze: Fundamentals of Aerosol Behavior, Wiley, New York, 1979.
,[18] Existence of gelling solutions for coagulation-fragmentation equations, Comm. Math. Phys. 194 (1998) 541-567. | MR | Zbl
,[19] Proof of dynamical scaling in Smoluchowski's coagulation equation with constant kernel, J. Statist. Phys. 75 (1994) 389-407. | MR | Zbl
, ,[20] From the discrete to the continuous coagulation-fragmentation equations, Proc. Roy. Soc. Edinburgh Sect. A 132 (5) (2002) 1219-1248. | MR | Zbl
, ,[21] The continuous coagulation-fragmentation equations with diffusion, Arch. Rational Mech. Anal. 162 (2002) 45-99. | MR | Zbl
, ,[22] Lê Châu-Hoàn, Etude de la classe des opérateurs m-accrétifs de et accrétifs dans , Thèse de 3ème cycle, Université de Paris VI, 1977.
[23] On coalescence equations and related models, in: , , (Eds.), Modelling and Computational Methods for Kinetic Equations, Modeling and Simulation in Science, Engineering and Technology (MSSET), Birkhäuser, 2004, pp. 321-356. | MR | Zbl
, ,[24] P. Laurençot, S. Mischler, Coagulation and fragmentation equations, in preparation.
[25] A survey on numerical solutions to the coagulation equation, J. Phys. A 34 (2001) 10219. | Zbl
,[26] Existence and properties of post-gel solutions for the kinetic equations of coagulation, J. Phys. A 16 (1983) 2861-2873. | MR
,[27] Scaling theory and exactly solved models in the kinetics of irreversible aggregation, Phys. Rep. 383 (2-3) (2003) 95-212.
,[28] The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids 19 (1961) 35-50.
, ,[29] Nucleation burst in coagulating system, Phys. Rev. E 62 (2000) 4932-4939.
, ,[30] “Shattering” Transition in Fragmentation, Phys. Rev. Lett. 58 (1987) 892.
, ,[31] Approach to self-similarity in Smoluchowski's coagulation equation, Comm. Pure Appl. Math. 57 (9) (2004) 1197-1232. | MR | Zbl
, ,[32] G. Menon, R.L. Pego, Dynamical scaling in Smoluchowski's coagulation equation: uniform convergence, Preprint, 2003.
[33] Existence globale pour l'équation de Smoluchowski continue non homogène et comportement asymptotique des solutions, C. R. Acad. Sci. Paris, Ser. I Math. 336 (2003) 407-412. | MR | Zbl
, ,[34] S. Mischler, Une introduction aux modèles de coagulation et fragmentation, Notes de cours de DEA, http://www.ceremade.dauphine.fr/~mischler/.
[35] On the spatially homogeneous Boltzmann equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (4) (1999) 467-501. | EuDML | Numdam | MR | Zbl
, ,[36] N. Morgan, C. Wells, M. Kraft, W. Wagner, Modelling nanoparticle dynamics: coagulation, sintering, particle inception and surface growth, Preprint No. 19, Cambridge Center for Computational Chemical Engineering, 2003.
[37] Cluster coagulation, Comm. Math. Phys. 209 (2000) 407-435. | MR | Zbl
,[38] Smoluchowski's coagulation equation: uniqueness, non-uniqueness and a hydrodynamic limit for the stochastic coalescent, Ann. Appl. Probab. 9 (1999) 78-109. | MR | Zbl
,[39] Atmospheric Chemistry and Physics of Air Pollution, John Wiley & Sons, New York, 1986.
,[40] Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen, Physik Z. 17 (1916) 557-599.
,[41] Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen, Z. Physik. Chemie 92 (1917) 129-168.
,[42] A global existence theorem for the general coagulation-fragmentation equation with unbounded kernels, Math. Methods Appl. Sci. 11 (1989) 627-648. | MR | Zbl
,[43] A uniqueness theorem for the coagulation-fragmentation equation, Math. Proc. Cambridge Philos. Soc. 107 (1990) 573-578. | MR | Zbl
,[44] A Maxwellian lower bound for solutions to the Boltzmann equation, Comm. Math. Phys. 183 (1997) 145-160. | MR | Zbl
, ,Cited by Sources: