Edit Profile (opens in new tab) Bobylev, Alexandre Vasiljévitch Compute Distance To: Compute Author ID: bobylev.alexandre-vasiljevitch Published as: Bobylev, A. V.; Bobylev, Alexander V.; Bobylev, Alexander; Bobylev, Alexandre V.; Bobylëv, A. V.; Bobylev, A.; Bobylev, Alexandre Vasiljévitch more...less Documents Indexed: 101 Publications since 1975, including 1 Book 2 Contributions as Editor Co-Authors: 61 Co-Authors with 84 Joint Publications 1,459 Co-Co-Authors all top 5 Co-Authors 17 single-authored 14 Cercignani, Carlo 11 Potapenko, Irina F. 10 Martínez Gamba, Irene 10 Spiga, Giampiero 4 Rjasanow, Sergej 4 Vinerean, Mirela C. 3 Illner, Reinhard 3 Karpov, S. A. 3 Toscani, Giuseppe 3 Victory, Harold Dean jun. 3 Windfäll, Åsa 2 Bernhoff, Niclas 2 Caraffini, Gian Luca 2 Carrillo de la Plata, José Antonio 2 Chuyanov, V. A. 2 Dukes, Peter James 2 Gabetta, Ester 2 Groppi, Maria 2 Hansen, Alex 2 Hauge, E. Hiis 2 Ibragimov, Nail Hairullovich 2 Meleshko, Sergey V. 2 Mossberg, Eva 2 Palczewski, Andrzej 2 Pareschi, Lorenzo 2 Schneider, Jacques 2 Struckmeier, Jens 1 Acedo, Luis 1 Aoki, Kazuo 1 Bisi, Marzia 1 Brantov, Andrei 1 Bychenkov, Valerii 1 Cassinari, Maria Paola 1 Desvillettes, Laurent 1 Dolgosheina, Elena B. 1 Dorodnitsyn, Vladimir A. 1 Esposito, Raffaele 1 Frosali, Giovanni 1 Grzhibovskis, Richards 1 Heintz, Alexei G. 1 Karpov, Stanislav 1 Karulin, Alex Yu. 1 Lebowitz, Joel Louis 1 Maaø, Frank A. 1 Monaco, Roberto 1 Nota, Alessia 1 Ostmo, Svend 1 Panferov, Vladislav A. 1 Piasecki, Jarosław 1 Pulvirenti, Mario 1 Saffirio, Chiara 1 Santos, Andrés 1 Sone, Yoshio 1 Sugimoto, Hiroshi 1 Takata, Shigeru 1 Vedenyapin, Victor V. 1 Velázquez, Juan J. L. 1 Yaroshevskij, V. A. 1 Ytrehus, Tor 1 Zhang, Chenglong 1 Zubarev, Dmitriĭ Nikolaevich all top 5 Serials 32 Journal of Statistical Physics 8 Kinetic and Related Models 5 Transport Theory and Statistical Physics 4 Matematicheskoe Modelirovanie 3 Communications in Mathematical Physics 3 Applied Mathematics Letters 3 Physics of Fluids 3 European Journal of Mechanics. B. Fluids 2 Journal of Mathematical Physics 2 European Journal of Mechanics. B. Fluids 2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 Journal of Computational Physics 1 Mathematical Biosciences 1 Mathematical Methods in the Applied Sciences 1 Soviet Scientific Reviews. Section C 1 Theoretical and Mathematical Physics 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 SIAM Journal on Numerical Analysis 1 Soviet Mathematics. Doklady 1 Acta Applicandae Mathematicae 1 Forum Mathematicum 1 Journal of Physics A: Mathematical and General 1 SIAM Journal on Applied Mathematics 1 Soviet Physics. Doklady 1 U.S.S.R. Computational Mathematics and Mathematical Physics 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Continuum Mechanics and Thermodynamics 1 Journal of Computer and Systems Sciences International 1 Institut Prikladnoĭ Matematiki Imeni M. V. Keldysha Rossiĭskoĭ Akademii Nauk. Moskva. Preprint 1 Rivista di Matematica della Università di Parma. Serie V 1 Mathematical Modeling and Computational Experiment 1 Discrete and Continuous Dynamical Systems 1 Rivista di Matematica della Università di Parma. Serie 6 1 Journal of Nonlinear Mathematical Physics 1 Rivista di Matematica della Università di Parma. Serie 7 1 Communications in Mathematical Sciences 1 Rivista di Matematica della Università di Parma. Serie 8 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 De Gruyter Series in Applied and Numerical Mathematics all top 5 Fields 76 Fluid mechanics (76-XX) 64 Statistical mechanics, structure of matter (82-XX) 28 Partial differential equations (35-XX) 10 Integral equations (45-XX) 9 Numerical analysis (65-XX) 3 Optics, electromagnetic theory (78-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Ordinary differential equations (34-XX) 2 Integral transforms, operational calculus (44-XX) 2 Mechanics of particles and systems (70-XX) 2 Astronomy and astrophysics (85-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Number theory (11-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 85 Publications have been cited 1,143 times in 588 Documents Cited by ▼ Year ▼ The theory of the nonlinear spatially uniform Boltzmann equation for Maxwell molecules. Zbl 0850.76619Bobylev, A. V. 94 1988 On some properties of kinetic and hydrodynamic equations for inelastic interactions. Zbl 1056.76071Bobylev, A. V.; Carrillo, J. A.; Gamba, I. M. 86 2000 Moment inequalities and high-energy tails for Boltzmann equations with inelastic interactions. Zbl 1097.82021Bobylev, A. V.; Gamba, I. M.; Panferov, V. A. 60 2004 Self-similar asymptotics for the Boltzmann equation with inelastic and elastic interactions. Zbl 1134.82324Bobylev, A. V.; Cercignani, C. 48 2003 A consistency result for a discrete-velocity model of the Boltzmann equation. Zbl 0895.76083Palczewski, Andrzej; Schneider, Jacques; Bobylev, Alexandre V. 45 1997 Fast deterministic method of solving the Boltzmann equation for hard spheres. Zbl 0965.76059Bobylev, A. V.; Rjasanow, S. 38 1999 Moment inequalities for the Boltzmann equation and applications to spatially homogneous problems. Zbl 0979.82049Bobylev, A. V. 38 1997 Difference scheme for the Boltzmann equation based on the fast Fourier transform. Zbl 0881.76061Bobylev, A.; Rjasanow, S. 37 1997 Inappropriateness of the heat-conduction equation for description of a temperature field of a stationary gas in the continuum limit: Examination by asymptotic analysis and numerical computation of the Boltzmann equation. Zbl 1027.76649Sone, Yoshio; Aoki, Kazuo; Takata, Shigeru; Sugimoto, Hiroshi; Bobylev, A. V. 32 1996 On approximation of the Boltzmann equation by discrete velocity models. Zbl 0834.76078Bobylev, Alexandre Vasiljévitch; Palczewski, Andrzej; Schneider, Jacques 30 1995 Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials. Zbl 1119.82318Bobylev, A. V.; Cercignani, C.; Toscani, G. 30 2003 On the self-similar asymptotics for generalized nonlinear kinetic Maxwell models. Zbl 1192.35126Bobylev, A. V.; Cercignani, C.; Gamba, I. M. 27 2009 From particle systems to the Landau equation: a consistency result. Zbl 1273.35281Bobylev, A. V.; Pulvirenti, M.; Saffirio, C. 27 2013 Instabilities in the Chapman-Enskog expansion and hyperbolic Burnett equations. Zbl 1134.82031Bobylev, A. V. 26 2006 Boltzmann equations for mixtures of Maxwell gases: exact solutions and power like tails. Zbl 1134.82032Bobylev, A. V.; Gamba, I. M. 23 2006 Moment equations for a granular material in a thermal bath. Zbl 1001.82092Bobylev, A. V.; Cercignani, C. 23 2002 Fourier transform method in the theory of the Boltzmann equation for Maxwellian molecules. Zbl 0361.76077Bobylev, A. V. 22 1975 Self-similar solutions of the Boltzmann equation and their applications. Zbl 1001.82091Bobylev, A. V.; Cercignani, C. 20 2002 Exact solutions of the Boltzmann equation. Zbl 0361.76082Bobylev, A. V. 19 1975 Quasistationary hydrodynamics for the Boltzmann equation. Zbl 1081.82612Bobylëv, A. V. 18 1995 A general consistent BGK model for gas mixtures. Zbl 1405.76042Bobylev, Alexander V.; Bisi, Marzia; Groppi, Maria; Spiga, Giampiero; Potapenko, Irina F. 17 2018 Exact eternal solutions of the Boltzmann equation. Zbl 1001.82090Bobylev, A. V.; Cercignani, C. 16 2002 The inverse Laplace transform of some analytic functions with an application to the eternal solutions of the Boltzmann equation. Zbl 1025.44002Bobylev, A. V.; Cercignani, C. 16 2002 On the rate of entropy production for the Boltzmann equation. Zbl 0958.82040Bobylev, Alexander V.; Cercignani, Carlo 15 1999 Exact solutions of the nonlinear Boltzmann equation and the theory of relaxation of a Maxwellian gas. Zbl 0565.76074Bobylev, A. V. 14 1984 Numerical solution of the Boltzmann equation using a fully conservative difference scheme based on the fast Fourier transform. Zbl 1017.82042Bobylev, A. V.; Rjasanow, S. 13 2000 On group invariant solutions of the Boltzmann equation. Zbl 0867.76077Bobylev, A. V.; Caraffini, G. L.; Spiga, G. 13 1996 Generalized Burnett hydrodynamics. Zbl 1144.82057Bobylev, A. V. 13 2008 Generalized kinetic Maxwell type models of granular gases. Zbl 1298.76209Bobylev, A. V.; Cercignani, C.; Gamba, I. M. 12 2008 Discrete velocity models without nonphysical invariants. Zbl 0958.82041Bobylev, Alexander V.; Cercignani, Carlo 12 1999 Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas. Zbl 1349.82071Bobylev, A. V.; Potapenko, I. F. 11 2013 On the generalization of the Boltzmann \(H\)-theorem for spatially homogeneous Maxwell gas. Zbl 0825.76713Bobylev, A. V.; Toscani, G. 10 1992 Construction of discrete kinetic models with given invariants. Zbl 1214.82087Bobylev, A. V.; Vinerean, M. C. 10 2008 Entropy inequalities for evaporation/condensation problem in rarefied gas dynamics. Zbl 0990.82022Bobylev, A. V.; Grzhibovskis, R.; Heintz, A. 9 2001 Discrete velocity models and dynamical systems. Zbl 1055.82018Bobylev, A. V.; Bernhoff, N. 9 2003 Weak shock waves for the general discrete velocity model of the Boltzmann equation. Zbl 1144.76051Bernhoff, Niclas; Bobylev, Alexander 9 2007 The Boltzmann equation and the group transformations. Zbl 0782.35078Bobylev, A. V. 9 1993 Discrete velocity models for mixtures. Zbl 0917.76075Bobylev, Alexander V.; Cercignani, Carlo 9 1998 On a class of exact two-dimensional stationary solutions for the Broadwell model of the Boltzmann equation. Zbl 0844.76084Bobylev, A. V.; Spiga, G. 8 1994 Exact solutions of discrete kinetic models and stationary problems for the plane Broadwell model. Zbl 0855.76064Bobylev, A. V. 8 1996 Boltzmann equation and hydrodynamics at the Burnett level. Zbl 1247.35195Bobylev, Alexander; Windfäll, Åsa 8 2012 Upper Maxwellian bounds for the Boltzmann equation with pseudo-Maxwell molecules. Zbl 1353.76075Bobylev, Alexander V.; Gamba, Irene M. 8 2017 Kinetic equations of the Landau type as a model of the Boltzmann equation and completely conservative difference schemes. Zbl 0493.76078Bobylev, A. V.; Potapenko, I. F.; Chuyanov, V. A. 7 1980 On some properties of the Landau kinetic equation. Zbl 1333.35151Bobylev, Alexander; Gamba, Irene; Potapenko, Irina 7 2015 The error of the splitting scheme for solving evolutionary equations. Zbl 0976.65081Bobylev, A. V.; Ohwada, T. 7 2001 Intenconnectivity of symmetry properties for equations of dynamics, kinetic theory of gases, and hydrodynamics. Zbl 0974.76580Bobylev, A. V.; Ibragimov, N. Kh. 7 1989 On Vlasov-Manev equations. I: Foundations, properties, and nonglobal existence. Zbl 0917.45007Bobylev, A. V.; Dukes, P.; Illner, R.; Victory, H. D. jun. 7 1997 From the Liouville equation to the generalized Boltzmann equation for magnetotransport in the 2D Lorentz model. Zbl 0990.82021Bobylev, A. V.; Hansen, Alex; Piasecki, J.; Hauge, E. H. 6 2001 Two-dimensional half-space problems for the Broadwell discrete velocity model. Zbl 0880.76068Bobylev, A. V.; Toscani, G. 6 1996 A class of invariant solutions of the Boltzmann equation. Zbl 0358.45007Bobylev, A. V. 6 1976 Implicit and iterative methods for the Boltzmann equation. Zbl 0854.76077Bobylev, A. V.; Struckmeier, J. 5 1996 Shock wave structure for generalized Burnett equations. Zbl 1308.76157Bobylev, A. V.; Bisi, M.; Cassinari, M. P.; Spiga, G. 5 2011 On some properties of linear and linearized Boltzmann collision operators for hard spheres. Zbl 1157.82369Bobylev, A. V.; Mossberg, E. 5 2008 Deterministic and stochastic methods for nonlinear Landau-Fokker-Planck kinetic equations with applications to plasma physics. Zbl 1165.82021Potapenko, I. F.; Bobylev, A. V.; Mossberg, E. 5 2008 On a model transport equation with inelastic scattering. Zbl 0907.76074Bobylev, A. V.; Spiga, G. 5 1998 Discrete velocity models of the Boltzmann equation and conservation laws. Zbl 1186.82068Bobylev, Alexander; Vinerean, Mirela; Windfäll, Åsa 5 2010 Erratum on: On some properties of kinetic and hydrodynamic equations for inelastic interactions”. Zbl 1126.82323Bobylev, A. V.; Carrillo, J. A.; Gamba, I. M. 4 2001 Non-stationary two-dimensional potential flows by the Broadwell model equations. Zbl 0963.76075Bobylev, Alexandre V.; Caraffini, Gian Luca; Spiga, Giampiero 4 2000 Qualitative analysis of the Navier-Stokes equations for evaporation-condensation problems. Zbl 1027.76672Bobylev, A. V.; Østmo, S.; Ytrehus, T. 4 1996 On the rate of relaxation for the Landau kinetic equation and related models. Zbl 1377.35202Bobylev, Alexander; Gamba, Irene M.; Zhang, Chenglong 4 2017 On the derivation of a high-velocity tail from the Boltzmann-Fokker-Planck equation for shear flow. Zbl 1159.82316Acedo, L.; Santos, A.; Bobylev, A. V. 4 2002 On Vlasov-Manev equations. II: Local existence and uniqueness. Zbl 0938.45008Illner, R.; Victory, H. D.; Dukes, P.; Bobylev, A. V. 4 1998 Self-similar asymptotics for a modified Maxwell-Boltzmann equation in systems subject to deformations. Zbl 1454.82032Bobylev, Alexander; Nota, Alessia; Velázquez, Juan J. L. 3 2020 Approximate solutions to the problem of stationary shear flow of smooth granular materials. Zbl 1001.76108Bobylev, Alexander V.; Groppi, Maria; Spiga, Giampiero 3 2002 Numerical simulation of the stationary one-dimensional Boltzmann equation by particle methods. Zbl 0864.76082Bobylev, A. V.; Struckmeier, J. 3 1996 Symmetries of evolution equations with non-local operators and applications to the Boltzmann equation. Zbl 1173.76042Bobylev, Alexander; Dorodnitsyn, Vladimir 3 2009 There is more to be learned from the Lorentz model. Zbl 0945.82554Bobylev, A. V.; Maaø, Frank A.; Hansen, Alex; Hauge, E. H. 3 1997 Boltzmann equation and hydrodynamics beyond Navier-Stokes. Zbl 1470.76013Bobylev, A. V. 3 2018 Long wave asymptotics for the Vlasov-Poisson-Landau kinetic equation. Zbl 1419.82065Bobylev, A. V.; Potapenko, I. F. 2 2019 Kinetic equations. Volume 1: Boltzmann equation, Maxwell models, and hydrodynamics beyond Navier-Stokes. Zbl 1460.35001Bobylev, Alexander V. 2 2020 Construction and classification of discrete kinetic models without spurious invariants. Zbl 1143.82023Bobylev, A. V.; Vinerean, M. C. 2 2007 Monte-Carlo method for two component plasmas. Zbl 1289.76077Bobylev, A. V.; Potapenko, I. F.; Karpov, S. A. 2 2012 On the generalization of Strang’s splitting scheme. Zbl 0959.65073Bobylev, A. V.; Ohwada, T. 2 1999 Collision integrals for attractive potentials. Zbl 0964.82045Bobylev, Alexander V.; Illner, Reinhard 2 1999 On stationary solutions to plane Broadwell model. Zbl 0815.35092Bobylev, A. V.; Gabetta, E.; Pareschi, L. 2 1995 Group analysis of the generalized Burnett equations. Zbl 1436.35019Bobylev, Alexander V.; Meleshko, Sergey V. 2 2020 Self-similar solutions of the Boltzmann equation for non-Maxwell molecules. Zbl 1034.82046Bobylev, A. V.; Cercignani, C. 2 2002 Exact and asymptotic stationary solutions of the semicontinuous Boltzmann equation. Zbl 0855.76065Bobylev, A. V.; Spiga, G. 1 1996 On a boundary value problem for the plane Broadwell model. Exact solutions and numerical simulation. Zbl 0833.76066Bobylev, A. V.; Gabetta, E.; Pareschi, L. 1 1995 DSMC modeling of a single hot spot evolution using the Landau-Fokker-Planck equation. Zbl 1307.82025Bobylev, Alexander; Brantov, Andrei; Bychenkov, Valerii; Karpov, Stanislav; Potapenko, Irina 1 2014 Relationships between the symmetry properties of the equations of gas kinetics and hydrodynamics. Zbl 1039.82507Bobylëv, A. V.; Ibragimov, N. Kh. 1 1993 Kinetic modeling of economic games with large number of participants. Zbl 1216.91020Bobylev, Alexander; Windfäll, Åsa 1 2011 On the maximum principle for discrete models of the Boltzmann equation and on the connection between the direct and inverse collision integrals of this equation. Zbl 0372.35072Bobylev, A. V.; Vedenjapin, V. V. 1 1977 Discrete kinetic models and conservation laws. Zbl 1232.82014Bobylev, Alexander V.; Vinerean, Mirela C. 1 2006 On group symmetries of the hydrodynamic equations for rarefied gas. Zbl 1476.35194Bobylev, Alexander V.; Meleshko, Sergey V. 1 2021 On group symmetries of the hydrodynamic equations for rarefied gas. Zbl 1476.35194Bobylev, Alexander V.; Meleshko, Sergey V. 1 2021 Self-similar asymptotics for a modified Maxwell-Boltzmann equation in systems subject to deformations. Zbl 1454.82032Bobylev, Alexander; Nota, Alessia; Velázquez, Juan J. L. 3 2020 Kinetic equations. Volume 1: Boltzmann equation, Maxwell models, and hydrodynamics beyond Navier-Stokes. Zbl 1460.35001Bobylev, Alexander V. 2 2020 Group analysis of the generalized Burnett equations. Zbl 1436.35019Bobylev, Alexander V.; Meleshko, Sergey V. 2 2020 Long wave asymptotics for the Vlasov-Poisson-Landau kinetic equation. Zbl 1419.82065Bobylev, A. V.; Potapenko, I. F. 2 2019 A general consistent BGK model for gas mixtures. Zbl 1405.76042Bobylev, Alexander V.; Bisi, Marzia; Groppi, Maria; Spiga, Giampiero; Potapenko, Irina F. 17 2018 Boltzmann equation and hydrodynamics beyond Navier-Stokes. Zbl 1470.76013Bobylev, A. V. 3 2018 Upper Maxwellian bounds for the Boltzmann equation with pseudo-Maxwell molecules. Zbl 1353.76075Bobylev, Alexander V.; Gamba, Irene M. 8 2017 On the rate of relaxation for the Landau kinetic equation and related models. Zbl 1377.35202Bobylev, Alexander; Gamba, Irene M.; Zhang, Chenglong 4 2017 On some properties of the Landau kinetic equation. Zbl 1333.35151Bobylev, Alexander; Gamba, Irene; Potapenko, Irina 7 2015 DSMC modeling of a single hot spot evolution using the Landau-Fokker-Planck equation. Zbl 1307.82025Bobylev, Alexander; Brantov, Andrei; Bychenkov, Valerii; Karpov, Stanislav; Potapenko, Irina 1 2014 From particle systems to the Landau equation: a consistency result. Zbl 1273.35281Bobylev, A. V.; Pulvirenti, M.; Saffirio, C. 27 2013 Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas. Zbl 1349.82071Bobylev, A. V.; Potapenko, I. F. 11 2013 Boltzmann equation and hydrodynamics at the Burnett level. Zbl 1247.35195Bobylev, Alexander; Windfäll, Åsa 8 2012 Monte-Carlo method for two component plasmas. Zbl 1289.76077Bobylev, A. V.; Potapenko, I. F.; Karpov, S. A. 2 2012 Shock wave structure for generalized Burnett equations. Zbl 1308.76157Bobylev, A. V.; Bisi, M.; Cassinari, M. P.; Spiga, G. 5 2011 Kinetic modeling of economic games with large number of participants. Zbl 1216.91020Bobylev, Alexander; Windfäll, Åsa 1 2011 Discrete velocity models of the Boltzmann equation and conservation laws. Zbl 1186.82068Bobylev, Alexander; Vinerean, Mirela; Windfäll, Åsa 5 2010 On the self-similar asymptotics for generalized nonlinear kinetic Maxwell models. Zbl 1192.35126Bobylev, A. V.; Cercignani, C.; Gamba, I. M. 27 2009 Symmetries of evolution equations with non-local operators and applications to the Boltzmann equation. Zbl 1173.76042Bobylev, Alexander; Dorodnitsyn, Vladimir 3 2009 Generalized Burnett hydrodynamics. Zbl 1144.82057Bobylev, A. V. 13 2008 Generalized kinetic Maxwell type models of granular gases. Zbl 1298.76209Bobylev, A. V.; Cercignani, C.; Gamba, I. M. 12 2008 Construction of discrete kinetic models with given invariants. Zbl 1214.82087Bobylev, A. V.; Vinerean, M. C. 10 2008 On some properties of linear and linearized Boltzmann collision operators for hard spheres. Zbl 1157.82369Bobylev, A. V.; Mossberg, E. 5 2008 Deterministic and stochastic methods for nonlinear Landau-Fokker-Planck kinetic equations with applications to plasma physics. Zbl 1165.82021Potapenko, I. F.; Bobylev, A. V.; Mossberg, E. 5 2008 Weak shock waves for the general discrete velocity model of the Boltzmann equation. Zbl 1144.76051Bernhoff, Niclas; Bobylev, Alexander 9 2007 Construction and classification of discrete kinetic models without spurious invariants. Zbl 1143.82023Bobylev, A. V.; Vinerean, M. C. 2 2007 Instabilities in the Chapman-Enskog expansion and hyperbolic Burnett equations. Zbl 1134.82031Bobylev, A. V. 26 2006 Boltzmann equations for mixtures of Maxwell gases: exact solutions and power like tails. Zbl 1134.82032Bobylev, A. V.; Gamba, I. M. 23 2006 Discrete kinetic models and conservation laws. Zbl 1232.82014Bobylev, Alexander V.; Vinerean, Mirela C. 1 2006 Moment inequalities and high-energy tails for Boltzmann equations with inelastic interactions. Zbl 1097.82021Bobylev, A. V.; Gamba, I. M.; Panferov, V. A. 60 2004 Self-similar asymptotics for the Boltzmann equation with inelastic and elastic interactions. Zbl 1134.82324Bobylev, A. V.; Cercignani, C. 48 2003 Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials. Zbl 1119.82318Bobylev, A. V.; Cercignani, C.; Toscani, G. 30 2003 Discrete velocity models and dynamical systems. Zbl 1055.82018Bobylev, A. V.; Bernhoff, N. 9 2003 Moment equations for a granular material in a thermal bath. Zbl 1001.82092Bobylev, A. V.; Cercignani, C. 23 2002 Self-similar solutions of the Boltzmann equation and their applications. Zbl 1001.82091Bobylev, A. V.; Cercignani, C. 20 2002 Exact eternal solutions of the Boltzmann equation. Zbl 1001.82090Bobylev, A. V.; Cercignani, C. 16 2002 The inverse Laplace transform of some analytic functions with an application to the eternal solutions of the Boltzmann equation. Zbl 1025.44002Bobylev, A. V.; Cercignani, C. 16 2002 On the derivation of a high-velocity tail from the Boltzmann-Fokker-Planck equation for shear flow. Zbl 1159.82316Acedo, L.; Santos, A.; Bobylev, A. V. 4 2002 Approximate solutions to the problem of stationary shear flow of smooth granular materials. Zbl 1001.76108Bobylev, Alexander V.; Groppi, Maria; Spiga, Giampiero 3 2002 Self-similar solutions of the Boltzmann equation for non-Maxwell molecules. Zbl 1034.82046Bobylev, A. V.; Cercignani, C. 2 2002 Entropy inequalities for evaporation/condensation problem in rarefied gas dynamics. Zbl 0990.82022Bobylev, A. V.; Grzhibovskis, R.; Heintz, A. 9 2001 The error of the splitting scheme for solving evolutionary equations. Zbl 0976.65081Bobylev, A. V.; Ohwada, T. 7 2001 From the Liouville equation to the generalized Boltzmann equation for magnetotransport in the 2D Lorentz model. Zbl 0990.82021Bobylev, A. V.; Hansen, Alex; Piasecki, J.; Hauge, E. H. 6 2001 Erratum on: On some properties of kinetic and hydrodynamic equations for inelastic interactions”. Zbl 1126.82323Bobylev, A. V.; Carrillo, J. A.; Gamba, I. M. 4 2001 On some properties of kinetic and hydrodynamic equations for inelastic interactions. Zbl 1056.76071Bobylev, A. V.; Carrillo, J. A.; Gamba, I. M. 86 2000 Numerical solution of the Boltzmann equation using a fully conservative difference scheme based on the fast Fourier transform. Zbl 1017.82042Bobylev, A. V.; Rjasanow, S. 13 2000 Non-stationary two-dimensional potential flows by the Broadwell model equations. Zbl 0963.76075Bobylev, Alexandre V.; Caraffini, Gian Luca; Spiga, Giampiero 4 2000 Fast deterministic method of solving the Boltzmann equation for hard spheres. Zbl 0965.76059Bobylev, A. V.; Rjasanow, S. 38 1999 On the rate of entropy production for the Boltzmann equation. Zbl 0958.82040Bobylev, Alexander V.; Cercignani, Carlo 15 1999 Discrete velocity models without nonphysical invariants. Zbl 0958.82041Bobylev, Alexander V.; Cercignani, Carlo 12 1999 On the generalization of Strang’s splitting scheme. Zbl 0959.65073Bobylev, A. V.; Ohwada, T. 2 1999 Collision integrals for attractive potentials. Zbl 0964.82045Bobylev, Alexander V.; Illner, Reinhard 2 1999 Discrete velocity models for mixtures. Zbl 0917.76075Bobylev, Alexander V.; Cercignani, Carlo 9 1998 On a model transport equation with inelastic scattering. Zbl 0907.76074Bobylev, A. V.; Spiga, G. 5 1998 On Vlasov-Manev equations. II: Local existence and uniqueness. Zbl 0938.45008Illner, R.; Victory, H. D.; Dukes, P.; Bobylev, A. V. 4 1998 A consistency result for a discrete-velocity model of the Boltzmann equation. Zbl 0895.76083Palczewski, Andrzej; Schneider, Jacques; Bobylev, Alexandre V. 45 1997 Moment inequalities for the Boltzmann equation and applications to spatially homogneous problems. Zbl 0979.82049Bobylev, A. V. 38 1997 Difference scheme for the Boltzmann equation based on the fast Fourier transform. Zbl 0881.76061Bobylev, A.; Rjasanow, S. 37 1997 On Vlasov-Manev equations. I: Foundations, properties, and nonglobal existence. Zbl 0917.45007Bobylev, A. V.; Dukes, P.; Illner, R.; Victory, H. D. jun. 7 1997 There is more to be learned from the Lorentz model. Zbl 0945.82554Bobylev, A. V.; Maaø, Frank A.; Hansen, Alex; Hauge, E. H. 3 1997 Inappropriateness of the heat-conduction equation for description of a temperature field of a stationary gas in the continuum limit: Examination by asymptotic analysis and numerical computation of the Boltzmann equation. Zbl 1027.76649Sone, Yoshio; Aoki, Kazuo; Takata, Shigeru; Sugimoto, Hiroshi; Bobylev, A. V. 32 1996 On group invariant solutions of the Boltzmann equation. Zbl 0867.76077Bobylev, A. V.; Caraffini, G. L.; Spiga, G. 13 1996 Exact solutions of discrete kinetic models and stationary problems for the plane Broadwell model. Zbl 0855.76064Bobylev, A. V. 8 1996 Two-dimensional half-space problems for the Broadwell discrete velocity model. Zbl 0880.76068Bobylev, A. V.; Toscani, G. 6 1996 Implicit and iterative methods for the Boltzmann equation. Zbl 0854.76077Bobylev, A. V.; Struckmeier, J. 5 1996 Qualitative analysis of the Navier-Stokes equations for evaporation-condensation problems. Zbl 1027.76672Bobylev, A. V.; Østmo, S.; Ytrehus, T. 4 1996 Numerical simulation of the stationary one-dimensional Boltzmann equation by particle methods. Zbl 0864.76082Bobylev, A. V.; Struckmeier, J. 3 1996 Exact and asymptotic stationary solutions of the semicontinuous Boltzmann equation. Zbl 0855.76065Bobylev, A. V.; Spiga, G. 1 1996 On approximation of the Boltzmann equation by discrete velocity models. Zbl 0834.76078Bobylev, Alexandre Vasiljévitch; Palczewski, Andrzej; Schneider, Jacques 30 1995 Quasistationary hydrodynamics for the Boltzmann equation. Zbl 1081.82612Bobylëv, A. V. 18 1995 On stationary solutions to plane Broadwell model. Zbl 0815.35092Bobylev, A. V.; Gabetta, E.; Pareschi, L. 2 1995 On a boundary value problem for the plane Broadwell model. Exact solutions and numerical simulation. Zbl 0833.76066Bobylev, A. V.; Gabetta, E.; Pareschi, L. 1 1995 On a class of exact two-dimensional stationary solutions for the Broadwell model of the Boltzmann equation. Zbl 0844.76084Bobylev, A. V.; Spiga, G. 8 1994 The Boltzmann equation and the group transformations. Zbl 0782.35078Bobylev, A. V. 9 1993 Relationships between the symmetry properties of the equations of gas kinetics and hydrodynamics. Zbl 1039.82507Bobylëv, A. V.; Ibragimov, N. Kh. 1 1993 On the generalization of the Boltzmann \(H\)-theorem for spatially homogeneous Maxwell gas. Zbl 0825.76713Bobylev, A. V.; Toscani, G. 10 1992 Intenconnectivity of symmetry properties for equations of dynamics, kinetic theory of gases, and hydrodynamics. Zbl 0974.76580Bobylev, A. V.; Ibragimov, N. Kh. 7 1989 The theory of the nonlinear spatially uniform Boltzmann equation for Maxwell molecules. Zbl 0850.76619Bobylev, A. V. 94 1988 Exact solutions of the nonlinear Boltzmann equation and the theory of relaxation of a Maxwellian gas. Zbl 0565.76074Bobylev, A. V. 14 1984 Kinetic equations of the Landau type as a model of the Boltzmann equation and completely conservative difference schemes. Zbl 0493.76078Bobylev, A. V.; Potapenko, I. F.; Chuyanov, V. A. 7 1980 On the maximum principle for discrete models of the Boltzmann equation and on the connection between the direct and inverse collision integrals of this equation. Zbl 0372.35072Bobylev, A. V.; Vedenjapin, V. V. 1 1977 A class of invariant solutions of the Boltzmann equation. Zbl 0358.45007Bobylev, A. V. 6 1976 Fourier transform method in the theory of the Boltzmann equation for Maxwellian molecules. Zbl 0361.76077Bobylev, A. V. 22 1975 Exact solutions of the Boltzmann equation. Zbl 0361.76082Bobylev, A. V. 19 1975 all cited Publications top 5 cited Publications all top 5 Cited by 592 Authors 30 Toscani, Giuseppe 27 Bobylev, Alexandre Vasiljévitch 25 Martínez Gamba, Irene 20 Mouhot, Clément 16 Bisi, Marzia 14 Dimarco, Giacomo 13 Aoki, Kazuo 12 Pareschi, Lorenzo 11 Mischler, Stéphane 11 Morimoto, Yoshinori 11 Spiga, Giampiero 10 Gabetta, Ester 10 Regazzini, Eugenio 9 Alonso, Ricardo J. 9 Carlen, Eric Anders 9 Desvillettes, Laurent 9 Takata, Shigeru 9 Velázquez, Juan J. L. 9 Wennberg, Bernt 9 Yang, Tong 8 Brull, Stephane 8 Filbet, Francis 8 Nota, Alessia 8 Struchtrup, Henning 8 Xu, Chao-Jiang 7 Bernhoff, Niclas 7 Carrillo de la Plata, José Antonio 7 Lods, Bertrand 7 Özer, Teoman 7 Rjasanow, Sergej 7 Sone, Yoshio 7 Taguchi, Satoshi 6 Ansari, Alireza 6 Fournier, Nicolas 6 Golse, François 6 Groppi, Maria 6 Haack, Jeffrey R. 6 Hu, Jingwei 6 Loubère, Raphaël 6 Martalò, Giorgio 6 Mieussens, Luc 6 Rana, Anirudh Singh 6 Slemrod, Marshall 6 Torrilhon, Manuel 6 Ukai, Seiji 6 Vedenyapin, Victor V. 6 Yun, Seok-Bae 5 Bassetti, Federico 5 Cai, Zhenning 5 Carvalho, Maria Conceição 5 Hauck, Cory D. 5 Lemou, Mohammed 5 Li, Haoguang 5 Lu, Xuguang 5 Meng, Fei 5 Pavlović, Nataša 5 Strain, Robert M. 5 Taskovic, Maja 5 Winter, Raphael 5 Wu, Lei 5 Zhang, Yonghao 4 Alexandre, Radjesvarane 4 Babovsky, Hans 4 Banasiak, Jacek 4 Boscheri, Walter 4 Briant, Marc 4 Cercignani, Carlo 4 Cho, Yong-Kum 4 Degond, Pierre 4 Duan, Renjun 4 Esposito, Raffaele 4 Guo, Yan 4 Ha, Seung-Yeal 4 Ilyin, O. V. 4 Jang, Jin Woo 4 Klingenberg, Christian F. 4 Marra, Rossana 4 Ohwada, Taku 4 Pirner, Marlies 4 Potapenko, Irina F. 4 Pulvirenti, Ada 4 Pulvirenti, Mario 4 Rey, Thomas 4 Saint-Raymond, Laure 4 Wang, Yanli 4 Yan, Bokai 4 Yoshida, Hiroaki 4 Zanella, Mattia 4 Zhang, Xianwen 3 Adzhiev, S. Z. 3 Ampatzoglou, Ioakeim 3 Arkeryd, Leif O. 3 Bae, Gi-Chan 3 Caflisch, Russel E. 3 Cañizo, José Alfredo 3 Cordier, Stéphane 3 Crouseilles, Nicolas 3 Dolera, Emanuele 3 Einav, Amit 3 Escobedo Martínez, Miguel ...and 492 more Authors all top 5 Cited in 138 Serials 80 Journal of Statistical Physics 64 Journal of Computational Physics 27 Kinetic and Related Models 22 Communications in Mathematical Physics 21 Archive for Rational Mechanics and Analysis 18 Physics of Fluids 16 Transport Theory and Statistical Physics 13 Computers & Mathematics with Applications 13 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 12 Continuum Mechanics and Thermodynamics 10 Journal of Mathematical Physics 10 SIAM Journal on Scientific Computing 9 Journal of Functional Analysis 9 European Journal of Mechanics. B. Fluids 8 SIAM Journal on Mathematical Analysis 7 Journal of Fluid Mechanics 7 Journal of Mathematical Analysis and Applications 7 Theoretical and Mathematical Physics 7 Journal of Differential Equations 7 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 7 Computational Mathematics and Mathematical Physics 5 Computer Methods in Applied Mechanics and Engineering 5 Physica A 5 Probability Theory and Related Fields 5 Applied Mathematics Letters 5 Journal de Mathématiques Pures et Appliquées. 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Mathematical, Physical and Engineering Sciences 2 Communications in Contemporary Mathematics 2 Differential Equations 2 Communications on Pure and Applied Analysis 2 Analysis and Applications (Singapore) 2 Communications in Computational Physics 2 Networks and Heterogeneous Media 2 Analysis and Mathematical Physics 2 Mathematics and Mechanics of Complex Systems 2 Journal of Computational and Theoretical Transport 1 International Journal of Modern Physics B 1 Applicable Analysis 1 Journal of Applied Mathematics and Mechanics 1 Reports on Mathematical Physics 1 Wave Motion 1 Reviews in Mathematical Physics 1 Chaos, Solitons and Fractals 1 Journal of Geometry and Physics 1 The Annals of Probability 1 Applied Mathematics and Optimization 1 International Journal of Mathematics and Mathematical Sciences 1 Inventiones Mathematicae 1 Journal of Applied Probability 1 Journal of Computational and Applied Mathematics 1 Meccanica 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Ricerche di Matematica 1 Physica D 1 Applied Numerical Mathematics 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Revista Matemática Iberoamericana 1 Mathematical and Computer Modelling 1 Asymptotic Analysis 1 Forum Mathematicum 1 Journal of Integral Equations and Applications 1 Sugaku Expositions 1 Japan Journal of Industrial and Applied Mathematics 1 Applied Mathematical Modelling 1 Journal of Non-Equilibrium Thermodynamics 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Journal of Nonlinear Science ...and 38 more Serials all top 5 Cited in 42 Fields 365 Fluid mechanics (76-XX) 360 Statistical mechanics, structure of matter (82-XX) 269 Partial differential equations (35-XX) 104 Numerical analysis (65-XX) 45 Probability theory and stochastic processes (60-XX) 37 Integral equations (45-XX) 19 Classical thermodynamics, heat transfer (80-XX) 15 Biology and other natural sciences (92-XX) 13 Mechanics of deformable solids (74-XX) 12 Quantum theory (81-XX) 11 Operator theory (47-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Integral transforms, operational calculus (44-XX) 7 Special functions (33-XX) 7 Ordinary differential equations (34-XX) 6 Dynamical systems and ergodic theory (37-XX) 5 Real functions (26-XX) 5 Mechanics of particles and systems (70-XX) 5 Astronomy and astrophysics (85-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Information and communication theory, circuits (94-XX) 3 History and biography (01-XX) 3 Approximations and expansions (41-XX) 3 Optics, electromagnetic theory (78-XX) 3 Operations research, mathematical programming (90-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Topological groups, Lie groups (22-XX) 2 Measure and integration (28-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 General topology (54-XX) 2 Computer science (68-XX) 2 Geophysics (86-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Difference and functional equations (39-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year