Exact solutions of the nonlinear Boltzmann equation and the theory of relaxation of a Maxwellian gas
A. V. Bobylev

This publication is cited in the following articles:

1. Ricardo Alonso, Milana Čolić, “Regularity theory for the space homogeneous polyatomic Boltzmann flow”, Journal of Differential Equations, 461 (2026), 114128  
2. E. Başakoğlu, C. Sun, N. Tzvetkov, Y. Wang, “Local well-posedness for the periodic Boltzmann equation with constant collision kernel”, Journal of Functional Analysis, 2025, 111288  
3. S. O. Poleshkin, “Pseudo-adaptive Grid for the Boltzmann Solver Based on the Discrete Velocity Method”, Lobachevskii J Math, 46:9 (2025), 4443  
4. G. Z. Lotova, G. A. Mikhailov, S. V. Rogasinsky, “Study and Optimization of N-Particle Numerical Statistical Algorithm for Solving the Boltzmann Equation”, Comput. Math. and Math. Phys., 64:5 (2024), 1065  
5. Xuwen Chen, Justin Holmer, “Well/Ill-Posedness Bifurcation for the Boltzmann Equation with Constant Collision Kernel”, Ann. PDE, 10:2 (2024)  
6. M. A. Brutyan, U. G. Ibragimov, “Asymmetric Self-Similar Viscous Gas Flows in a Wedge”, Fluid Dyn, 57:7 (2022), 923  
7. Zhenning Cai, Yuwei Fan, Yanli Wang, “Burnett spectral method for the spatially homogeneous Boltzmann equation”, Computers & Fluids, 200 (2020), 104456  
8. Luca Romagnuolo, Ruochen Yang, Emma Frosina, Giorgio Rizzoni, Assunta Andreozzi, Adolfo Senatore, “Physical modeling of evaporative emission control system in gasoline fueled automobiles: A review”, Renewable and Sustainable Energy Reviews, 116 (2019), 109462  
9. M. A. Brutyan, P. L. Krapivsky, “Exact Solutions to the Steady Navier–Stokes Equations of Viscous Heat-Conducting Gas Flow Induced by the Plane Jet Issuing from the Line Source”, Fluid Dyn, 53:S2 (2018), 1  
10. Jean-Marie Barbaroux, Dirk Hundertmark, Tobias Ried, Semjon Vugalter, “Gevrey Smoothing for Weak Solutions of the Fully Nonlinear Homogeneous Boltzmann and Kac Equations Without Cutoff for Maxwellian Molecules”, Arch Rational Mech Anal, 225:2 (2017), 601  
11. Oleg Ilyin, “Exact Stationary and Non-stationary Solutions to Inelastic Maxwell Model with Infinite Energy”, J Stat Phys, 165:4 (2016), 755  
12. Bernard Shizgal, Scientific Computation, Spectral Methods in Chemistry and Physics, 2015, 247  
13. Bernard Shizgal, Scientific Computation, Spectral Methods in Chemistry and Physics, 2015, 109  
14. Evsevleeva L.G., Sverdlova O.L., Kirik M.S., Gozbenko V.E., “Analiticheskaya model vzaimodeistviya atomov kisloroda s poverkhnostyu adsorbenta”, Sovremennye tekhnologii. sistemnyi analiz. modelirovanie, 2012, no. 3, 137–140  
15. Christopher R. Schrock, Aihua W. Wood, “Distributional Monte Carlo Solution Technique for Rarefied Gasdynamics”, Journal of Thermophysics and Heat Transfer, 26:1 (2012), 185  
16. Christopher R. Schrock, Aihua W. Wood, “Distributional Monte Carlo Solution Technique for Rarefied Gasdynamics”, Journal of Thermophysics and Heat Transfer, 26:1 (2012), 185  
17. Malkov E.A., Ivanov M.S., “Determinirovannyi metod chastits-v-yacheikakh dlya resheniya zadach dinamiki razrezhennogo gaza. chast i”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 12:1 (2011), 368–374      
18. Mikhail Ivanov, Evgeniy Malkov, 42nd AIAA Thermophysics Conference, 2011  
19. Christopher Schrock, Aihua Wood, 42nd AIAA Thermophysics Conference, 2011  
20. Kinetic Boltzmann, Vlasov and Related Equations, 2011, 289  
21. Ricardo J. Alonso, Emanuel Carneiro, “Estimates for the Boltzmann collision operator via radial symmetry and Fourier transform”, Advances in Mathematics, 223:2 (2010), 511  
22. Yurii N. Grigoriev, Nail H. Ibragimov, Vladimir F. Kovalev, Sergey V. Meleshko, Lecture Notes in Physics, 806, Symmetries of Integro-Differential Equations, 2010, 57  
23. Emanuele Dolera, Eugenio Regazzini, “The role of the central limit theorem in discovering sharp rates of convergence to equilibrium for the solution of the Kac equation”, Ann. Appl. Probab., 20:2 (2010)  
24. Eugene Malkov, Michail Ivanov, 10th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, 2010  
25. Ester Gabetta, Eugenio Regazzini, “Central limit theorem for the solution of the Kac equation”, Ann. Appl. Probab., 18:6 (2008)  
26. M. A. Korotchenko, G. A. Mikhailov, S. V. Rogazinskii, “Modifications of weighted Monte Carlo algorithms for nonlinear kinetic equations”, Comput. Math. Math. Phys., 47:12 (2007), 2023–2033      
27. Eric Carlen, Ester Gabetta, Eugenio Regazzini, “On the Rate of Explosion for Infinite Energy Solutions of the Spatially Homogeneous Boltzmann Equation”, J Stat Phys, 129:4 (2007), 699  
28. A. L. KUZEMSKY, “THEORY OF TRANSPORT PROCESSES AND THE METHOD OF THE NONEQUILIBRIUM STATISTICAL OPERATOR”, Int. J. Mod. Phys. B, 21:17 (2007), 2821  
29. M. S. Ivanov, M. A. Korotchenko, G. A. Mikhailov, S. V. Rogazinskii, “Global weighted Monte Carlo method for the nonlinear Boltzmann equation”, Comput. Math. Math. Phys., 45:10 (2005), 1792–1801    
30. Seung-Yeal Ha, “L1-stability of the Boltzmann equation for Maxwellian molecules”, Nonlinearity, 18:3 (2005), 981  
31. Alexander N. Gorban, Ilya V. Karlin, Lecture Notes in Physics, 660, Invariant Manifolds for Physical and Chemical Kinetics, 2005, 469  
32. Isaac Goldhirsch, Mechanics for a New Mellennium, 2001, 345  
33. Isaac Goldhirsch, Lecture Notes in Physics, 564, Granular Gases, 2001, 79  
34. I. Goldhirsch, Handbook of Powder Technology, 10, Handbook of Conveying and Handling of Particulate Solids, 2001, 245  
35. V. V. Aristov, Fluid Mechanics and its Applications, 60, Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows, 2001, 139  
36. Isaac Goldhirsch, Modeling and Simulation in Science, Engineering and Technology, Modeling in Applied Sciences, 2000, 21  
37. J. A. Carrillo, C. Cercignani, I. M. Gamba, “Steady states of a Boltzmann equation for driven granular media”, Phys. Rev. E, 62:6 (2000), 7700  
38. I. Goldhirsch, Traffic and Granular Flow '99, 2000, 469  
39. I. Goldhirsch, T. P. C. van Noije, “Green-Kubo relations for granular fluids”, Phys. Rev. E, 61:3 (2000), 3241  
40. Laurent Desvillettes, “Regularization properties of the 2-dimensional non radially symmetric non cutoff spatially homogeneous Boltzmann equation for Maxwellian molecules”, Transport Theory and Statistical Physics, 26:3 (1997), 341  
41. Alexey K. Lopatin, “Symmetry in Nonlinear Mechanics: Averaging and Normalization Procedures, New Problems and Algorithms”, JNMP, 3:1-2 (1996), 111  
42. A. G. Bashkirov, A. V. Orlov, “Shock-wave structure for some nonanalytical in-velocity closures”, Phys. Rev. E, 53:1 (1996), R17  
43. A. A. Raines, “Numerical testing of Bird's VHS model”, Comput. Math. Math. Phys., 35:8 (1995), 1025–1031        
44. L. Desvillettes, “Some applications of the method of moments for the homogeneous Boltzmann and Kac equations”, Arch. Rational Mech. Anal., 123:4 (1993), 387  
45. M. A. Brutyan, P. L. Krapivskii, “Stability of periodic viscous gas flows”, Fluid Dyn, 27:1 (1992), 7  
46. V. V. Vedenyapin, “Differential forms in spaces without a norm. A theorem on the uniqueness of Boltzmann's $H$-function”, Russian Math. Surveys, 43:1 (1988), 193–219          
47. A. V. Mishchenko, D. Ya. Petrina, “Linearization and exact solutions of a class of Boltzmann equations”, Theoret. and Math. Phys., 77:1 (1988), 1096–1109