References
- Abramowitz , M. and Stegun , I. A. 1965 . Handbook of Mathematical Functions Edited by: Abramowitz , M. and Stegun , I. A. New York : Dover .
- Bisi , M. and Spiga , G. 2005 . Fluid‐dynamic equations for granular particles in a host medium . J. Math. Phys. , 46 : 113301 (1–20)
- Bisi , M. , Spiga , G. and Toscani , G. 2004 . Grad's equations and hydrodynamics for weakly inelastic granular flows . Phys. Fluids , 16 : 4235 – 4247 .
- Bobylev , A. V. , Carrillo , J. A. and Gamba , I. 2000 . On some properties of kinetic and hydrodynamic equations for inelastic interactions . J. Stat. Phys. , 98 : 743 – 773 .
- Brey , J. J. , Dufty , J. W. , Kim , C. S. and Santos , A. 1998 . Hydrodynamics for granular flows at low density . Phys. Rev. E , 58 : 4638 – 4653 .
- Brilliantov , N. V. and Pöschel , T. 2000 . “ Granular gases with impact‐velocity dependent restitution coefficient ” . In Granular Gases Edited by: Pöschel , T. and Luding , S. 100 – 124 . Berlin : Springer Verlag . Lecture Notes in Physics
- Brull , S. and Pareschi , L. 2006 . Dissipative hydrodynamic models for the diffusion of impurities in a gas . Appl. Math. Lett., , 19 : 516 – 526 .
- Carrillo , J. A. and Goudon , T. 2006 . Stability and asymptotic analysis of a fluid–particle interaction model . Comm. Partial Differential Equations, , 31 : 1349 – 1379 .
- Case , K. M. and Zweifel , P. F. 1967 . Linear Transport Theory Reading, MA : Addison‐Wesley .
- Cercignani , C. 1988 . The Boltzmann Equation and Its Applications New York : Springer .
- Chapman , S. and Cowling , T. G. 1970 . The Mathematical Theory of Non‐uniform Gases Cambridge : Cambridge University Press .
- Duderstadt , J. J. and Martin , W. R. 1979 . Transport Theory New York : John Wiley and Sons .
- Ernst , M. H. and Brito , R. 2002 . High energy tails for inelastic Maxwell models . Europhys. Lett. , 43 : 497 – 502 .
- Goldman , D. , Shattuck , M. D. , Bizon , C. , McCormick , W. D. , Swift , J. B. and Swinney , H. L. 1998 . Absence of inelastic collapse in a realistic three ball model . Phys. Rev. E , 57 : 4831 – 4833 .
- Goldshtein , A. and Shapiro , M. 1995 . Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations . J. Fluid Mech. , 282 : 75 – 114 .
- Goudon , T. , Jabin , P. E. and Vasseur , A. 2004a . Hydrodynamic limits for the Vlasov–Navier–Stokes equations: Light particles regime . Indiana Univ. Math. J. , 53 : 1495 – 1516 .
- Goudon , T. , Jabin , P. E. and Vasseur , A. 2004b . Hydrodynamic limits for the Vlasov–Navier–Stokes equations: Fine particles regime . Indiana Univ. Math. J. , 53 : 1517 – 1536 .
- Grad , H. 1949 . On the kinetic theory of rarefied gases . Comm. Pure Appl. Math. , 2 : 331 – 407 .
- Levermore , C. D. 1996 . Moment closure hierarchies for kinetic theories . J. Stat. Phys. , 83 : 1021 – 1065 .
- Lods , B. and Toscani , G. 2004 . The dissipative linear Boltzmann equation for hard spheres . J. Stat. Phys. , 117 : 635 – 664 .
- Majorana , A. 1991 . Space homogeneous solutions of the Boltzmann equation describing electron–phonon interactions in semiconductors . Transp. Theory Stat. Phys. , 20 : 261 – 279 .
- Martin , P. A. and Piasecki , J. 1999 . Thermalization of a particle by dissipative collisions . Europhys. Lett. , 46 : 613 – 616 .
- McNamara , S. and Young , W. R. 1993 . Kinetics of a one‐dimensional granular medium in the quasi‐elastic limit . Phys. Fluids A , 5 : 34 – 45 .
- Østmo , S. , Frezzotti , A. and Ytrehus , T. 1997 . Kinetic theory study of steady evaporation from a spherical condensed phase containing inert solid particles . Phys. Fluids , 9 : 211 – 225 .
- Pettersson , R. 2005 . On solutions to the linear Boltzmann equation for granular gases . Transp. Theory Stat. Phys. , 33 : 527 – 544 .
- Risso , D. and Cordero , P. 2002 . Dynamics of rarefied granular gases . Phys. Rev. E. , 65 : 021304 (1–9)
- Spiga , G. and Toscani , G. 2003 . The dissipative linear Boltzmann equation . Appl. Math. Letters , 17 : 295 – 301 .