Non zero flux solutions of kinetic equations
Escobedo, Miguel1
1 Departamento de Matemáticas Facultad de Ciencias y Tecnología Universidad del País Vasco Barrio Sarriena s/n 48940 Lejona (Vizcaya) Spain
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2009-2010), Exposé no. 20, 15 p.
Escobedo, Miguel 1

1 Departamento de Matemáticas Facultad de Ciencias y Tecnología Universidad del País Vasco Barrio Sarriena s/n 48940 Lejona (Vizcaya) Spain 
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Escobedo, Miguel. Non zero flux solutions of kinetic equations. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2009-2010), Exposé no. 20, 15 p. http://archive.numdam.org/item/SEDP_2009-2010____A20_0/

[1] R. Baier, T. Stockkamp, Kinetic equations for Bose-Einstein condensates from the 2PI effective action, arXiv:hep-ph/0412310.

[2] A. M. Balk, V. E. Zakharov, Stability of Weak-Turbulence Kolmogorov Spectra in Nonlinear Waves and Weak Turbulence, V. E. Zakharov Ed., A. M. S. Translations Series 2, Vol. 182, 1998, 1-81. | MR | Zbl

[3] W. H. Carothers, Faraday Soc. Trans. 32, 1936, 39–53.

[4] P. G. J. van Dongen, M.H. Ernst, Cluster size distribution in irreversible aggregation at large times J. Phys. A 18 (1985) 2779–2793. | MR

[5] P. G. J. van Dongen, On the possible ocurrence of instantaneous gelation in Smoluchowski’s coagulation equation, J. Phys. A: Math. Gen. 20 (1987), 1889–1904.

[6] P. B. Dubovski, I. W. Stewart, Existence, Uniqueness and Mass Conservation for the Coagulation-Fragmentation Equation, Math. Meth. Appl. Sciences 19, (1996), 571–591. | MR | Zbl

[7] M. H. Ernst, R. M. Ziff & E. M. Hendriks, Coagulation processes with a phase transition, J. of Colloid and Interface Sci. 97, (1984), 266–277.

[8] M. Escobedo, S. Mischler & B. Perthame, Gelation in coagulation and fragmentation models. Commun. Math. Phys. 231 (2002) 1, 157-188. | MR | Zbl

[9] M. Escobedo, S. Mischler & J. J. L. Velázquez, On the fundamental solution of the linearized Uehling-Uhlenbeck equation, Arch. Rat. Mech. Anal. 186, (2007), 309–349. | MR

[10] M. Escobedo, S. Mischler & J. J. L. Velázquez, Singular Solutions for the Uehling Uhlenbeck Equation, Proc. Roy. Soc. Edinburgh, 138A, (2008), 67–107. | MR | Zbl

[11] M. Escobedo, & J. J. L. Velázquez, On a linearised coagulation equation, Commun. Math. Phys. 297 3, (2010) 237–267.

[12] M. Escobedo, & J. J. L. Velázquez, Local well posedness for a linear coagulation equation, preprint 2009, arXiv:0911.1641. Submitted for publication.

[13] P. J. Flory, Molecular Size Distribution in Three Dimensional Polymers I, II, III. J. Am. Chem. Soc. 63 (1941) 3083–3100.

[14] P. J. Flory, Fundamental Principles of Condensation Polymerization. J. Phys. Chem. 46 (1942) 137-197.

[15] I. Jeon, Existence of gelling solutions for coagulation-fragmentation equations, Comm. Math. Phys. 194 (1998), 541–567. | MR | Zbl

[16] F. Leyvraz, Scaling Theory and Exactly Solved Models in the Kinetics of Irreversible Aggregation, Phys. Reports 383 (2003) Issues 2-3, 95–212.

[17] F. Leyvraz, H. R. Tschudi, Singularities in the kinetics of coagulation processes, J. Phys. A 14, (1981), 3389–3405. | MR | Zbl

[18] X. Lu, The Boltzmann equation for Bose Einstein particles: Velocity concentration and convergence to equilibrium, J. Stat. Phys. 119, (2005), 1027–1067. | MR | Zbl

[19] N. I. Muskhelishvili, Singular Integral Equations. Translated from second edition, Moscow (1946) by J.R.M. Radok. Noordhof, Groningen. (1953) | MR | Zbl

[20] B. Noble, Methods based on the Wiener-Hopf Technique. Second edition, Chelsea Publishing Company, New York. (1988) | Zbl

[21] L. W. Nordheim, On the Kinetic Method in the New Statistics and its Applications in the Electron Theory of Conductivity, Proc. R. Soc. London A 119, (1928), 689–698.

[22] M. von Smoluchowski, Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen Z. Phys. 17 (1916), 557-585.

[23] H. Spohn, Kinetic of the Bose-Einstein condensation, Physica D, 239 (2010), 627–634. | MR | Zbl

[24] W. H. Stockmayer, Theory of Molecular Size Distribution and Gel Formation in Branched-Chain Polymers. J. Chem. Phys. 11 (1943) 45–55.

[25] E. A. Uehling, G. E. Uhlenbeck, Transport phenomena in Einstein-Bose and Fermi-Dirac gases, Physical Review 43 (1933) 552-561.

[26] E. Zaremba, T. Nikuni, A. Griffin, Dynamics of Trapped Bose Gases at Finite Temperatures J. Low Temp. Phys. 116 (1999).