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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika

TMF, 1984, Volume 60, Number 2, Pages 280–310 (Mi tmf5284)

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. 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  crossref
  2. Xuwen Chen, Justin Holmer, “Well/Ill-Posedness Bifurcation for the Boltzmann Equation with Constant Collision Kernel”, Ann. PDE, 10:2 (2024)  crossref
  3. M. A. Brutyan, U. G. Ibragimov, “Asymmetric Self-Similar Viscous Gas Flows in a Wedge”, Fluid Dyn, 57:7 (2022), 923  crossref
  4. Zhenning Cai, Yuwei Fan, Yanli Wang, “Burnett spectral method for the spatially homogeneous Boltzmann equation”, Computers & Fluids, 200 (2020), 104456  crossref
  5. 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  crossref
  6. 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  crossref
  7. 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  crossref
  8. Oleg Ilyin, “Exact Stationary and Non-stationary Solutions to Inelastic Maxwell Model with Infinite Energy”, J Stat Phys, 165:4 (2016), 755  crossref
  9. Bernard Shizgal, Scientific Computation, Spectral Methods in Chemistry and Physics, 2015, 247  crossref
  10. Bernard Shizgal, Scientific Computation, Spectral Methods in Chemistry and Physics, 2015, 109  crossref
  11. 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  elib
  12. Christopher R. Schrock, Aihua W. Wood, “Distributional Monte Carlo Solution Technique for Rarefied Gasdynamics”, Journal of Thermophysics and Heat Transfer, 26:1 (2012), 185  crossref
  13. Christopher R. Schrock, Aihua W. Wood, “Distributional Monte Carlo Solution Technique for Rarefied Gasdynamics”, Journal of Thermophysics and Heat Transfer, 26:1 (2012), 185  crossref
  14. 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  mathnet  mathnet  elib
  15. Mikhail Ivanov, Evgeniy Malkov, 42nd AIAA Thermophysics Conference, 2011  crossref
  16. Christopher Schrock, Aihua Wood, 42nd AIAA Thermophysics Conference, 2011  crossref
  17. Kinetic Boltzmann, Vlasov and Related Equations, 2011, 289  crossref
  18. Ricardo J. Alonso, Emanuel Carneiro, “Estimates for the Boltzmann collision operator via radial symmetry and Fourier transform”, Advances in Mathematics, 223:2 (2010), 511  crossref
  19. Yurii N. Grigoriev, Nail H. Ibragimov, Vladimir F. Kovalev, Sergey V. Meleshko, Lecture Notes in Physics, 806, Symmetries of Integro-Differential Equations, 2010, 57  crossref
  20. 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)  crossref
  21. Eugene Malkov, Michail Ivanov, 10th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, 2010  crossref
  22. Ester Gabetta, Eugenio Regazzini, “Central limit theorem for the solution of the Kac equation”, Ann. Appl. Probab., 18:6 (2008)  crossref
  23. 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  mathnet  crossref  mathscinet
  24. 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  crossref
  25. A. L. KUZEMSKY, “THEORY OF TRANSPORT PROCESSES AND THE METHOD OF THE NONEQUILIBRIUM STATISTICAL OPERATOR”, Int. J. Mod. Phys. B, 21:17 (2007), 2821  crossref
  26. 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  mathnet  mathscinet
  27. Seung-Yeal Ha, “L1-stability of the Boltzmann equation for Maxwellian molecules”, Nonlinearity, 18:3 (2005), 981  crossref
  28. Alexander N. Gorban, Ilya V. Karlin, Lecture Notes in Physics, 660, Invariant Manifolds for Physical and Chemical Kinetics, 2005, 469  crossref
  29. Isaac Goldhirsch, Mechanics for a New Mellennium, 2001, 345  crossref
  30. Isaac Goldhirsch, Lecture Notes in Physics, 564, Granular Gases, 2001, 79  crossref
  31. I. Goldhirsch, Handbook of Powder Technology, 10, Handbook of Conveying and Handling of Particulate Solids, 2001, 245  crossref
  32. V. V. Aristov, Fluid Mechanics and its Applications, 60, Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows, 2001, 139  crossref
  33. Isaac Goldhirsch, Modeling and Simulation in Science, Engineering and Technology, Modeling in Applied Sciences, 2000, 21  crossref
  34. 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  crossref
  35. I. Goldhirsch, Traffic and Granular Flow '99, 2000, 469  crossref
  36. I. Goldhirsch, T. P. C. van Noije, “Green-Kubo relations for granular fluids”, Phys. Rev. E, 61:3 (2000), 3241  crossref
  37. 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  crossref
  38. Alexey K. Lopatin, “Symmetry in Nonlinear Mechanics: Averaging and Normalization Procedures, New Problems and Algorithms”, JNMP, 3:1-2 (1996), 111  crossref
  39. A. G. Bashkirov, A. V. Orlov, “Shock-wave structure for some nonanalytical in-velocity closures”, Phys. Rev. E, 53:1 (1996), R17  crossref
  40. A. A. Raines, “Numerical testing of Bird's VHS model”, Comput. Math. Math. Phys., 35:8 (1995), 1025–1031  mathnet  mathscinet  zmath  isi
  41. L. Desvillettes, “Some applications of the method of moments for the homogeneous Boltzmann and Kac equations”, Arch. Rational Mech. Anal., 123:4 (1993), 387  crossref
  42. M. A. Brutyan, P. L. Krapivskii, “Stability of periodic viscous gas flows”, Fluid Dyn, 27:1 (1992), 7  crossref
  43. 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  mathnet  crossref  mathscinet  zmath  adsnasa
  44. 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  mathnet  crossref  mathscinet  zmath  isi


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