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On a relativistic Fokker-Planck equation in kinetic theory
On a model for mass aggregation with maximal size
1. | Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, Netherlands |
2. | Department of Mathematics, Saarland University, 66123 Saarbrücken, Germany |
3. | Oxford Centre of Nonlinear PDE, Mathematical Insitute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, United Kingdom |
4. | School of Computer and Communication Sciences, École polytechnique fédérale de Lausanne, CH - 1015 Lausanne, Switzerland |
References:
[1] |
A. Boudaoud, J. Bico and B. Roman, Elastocapillary coalescence: Aggregation and fragmentation with maximal size, Phys. Rev. E, 76 (2007), 060102.
doi: 10.1103/PhysRevE.76.060102. |
[2] |
R. L. Drake, A general mathematical survey of the coagulation equation, In G. M. Hidy and J. R. Brock eds., "Topics in current aerosol research (Part 2)"; International reviews in Aerosol Physics and Chemistry, Pergamon (1972), 201-376 |
[3] |
M. Escobedo, S. Mischler and M. Rodriguez Ricard, On self-similarity and stationary problems for fragmentation and coagulation models, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), 99-125. |
[4] |
N. Fournier and P. Laurençot, Existence of self-similar solutions to Smoluchowski's coagulation equation, Comm. Math. Phys., 256 (2005) 589-609.
doi: 10.1007/s00220-004-1258-5. |
[5] |
N. Fournier and P. Laurençot, Well-posedness of Smoluchowski's coagulation equation for a class of homogeneous kernels, J. Funct. Anal., 233 (2006) 351-379.
doi: 10.1016/j.jfa.2005.07.013. |
[6] |
S. K. Friedlander, "Smoke, Dust and Haze: Fundamentals of Aerosol Dynamics," Wiley, New York, 1977. |
[7] |
T. Gallay and A. Mielke, Convergence results for a coarsening model using global linearization, J. Nonlinear Science, 13 (2003), 311-346.
doi: 10.1007/s00332-002-0543-8. |
[8] |
F. Leyvraz, Scaling theory and exactly solvable models in the kinetics of irreversible aggregation, Phys. Reports, 383 (2003), 95-212.
doi: 10.1016/S0370-1573(03)00241-2. |
[9] |
G. Menon and R. L. Pego, Approach to self-similarity in Smoluchowski's coagulation equations, Comm. Pure Appl. Math., 57 (2004), 1197-1232.
doi: 10.1002/cpa.3048. |
[10] |
G. Menon, B. Niethammer and R. L. Pego, Dynamics and self-similarity in min-driven clustering, Trans. AMS, 362 (2010), 6551-6590.
doi: 10.1090/S0002-9947-2010-05085-8. |
[11] |
M. Smoluchowski, Drei vorträge über diffusion, brownsche molekularbewegung und koagulation von kolloidteilchen, Phys. Zeitschr., 17 (1916), 557-599. |
[12] |
R. M. Ziff, Kinetics of polymerization, J. Statist. Phys., 23 (1980), 241-263.
doi: 10.1007/BF01012594. |
show all references
References:
[1] |
A. Boudaoud, J. Bico and B. Roman, Elastocapillary coalescence: Aggregation and fragmentation with maximal size, Phys. Rev. E, 76 (2007), 060102.
doi: 10.1103/PhysRevE.76.060102. |
[2] |
R. L. Drake, A general mathematical survey of the coagulation equation, In G. M. Hidy and J. R. Brock eds., "Topics in current aerosol research (Part 2)"; International reviews in Aerosol Physics and Chemistry, Pergamon (1972), 201-376 |
[3] |
M. Escobedo, S. Mischler and M. Rodriguez Ricard, On self-similarity and stationary problems for fragmentation and coagulation models, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), 99-125. |
[4] |
N. Fournier and P. Laurençot, Existence of self-similar solutions to Smoluchowski's coagulation equation, Comm. Math. Phys., 256 (2005) 589-609.
doi: 10.1007/s00220-004-1258-5. |
[5] |
N. Fournier and P. Laurençot, Well-posedness of Smoluchowski's coagulation equation for a class of homogeneous kernels, J. Funct. Anal., 233 (2006) 351-379.
doi: 10.1016/j.jfa.2005.07.013. |
[6] |
S. K. Friedlander, "Smoke, Dust and Haze: Fundamentals of Aerosol Dynamics," Wiley, New York, 1977. |
[7] |
T. Gallay and A. Mielke, Convergence results for a coarsening model using global linearization, J. Nonlinear Science, 13 (2003), 311-346.
doi: 10.1007/s00332-002-0543-8. |
[8] |
F. Leyvraz, Scaling theory and exactly solvable models in the kinetics of irreversible aggregation, Phys. Reports, 383 (2003), 95-212.
doi: 10.1016/S0370-1573(03)00241-2. |
[9] |
G. Menon and R. L. Pego, Approach to self-similarity in Smoluchowski's coagulation equations, Comm. Pure Appl. Math., 57 (2004), 1197-1232.
doi: 10.1002/cpa.3048. |
[10] |
G. Menon, B. Niethammer and R. L. Pego, Dynamics and self-similarity in min-driven clustering, Trans. AMS, 362 (2010), 6551-6590.
doi: 10.1090/S0002-9947-2010-05085-8. |
[11] |
M. Smoluchowski, Drei vorträge über diffusion, brownsche molekularbewegung und koagulation von kolloidteilchen, Phys. Zeitschr., 17 (1916), 557-599. |
[12] |
R. M. Ziff, Kinetics of polymerization, J. Statist. Phys., 23 (1980), 241-263.
doi: 10.1007/BF01012594. |
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