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Volumn 114, Issue 5-6, 2004, Pages 1453-1480

Asymptotic properties of the inelastic Kac model

Author keywords

Boltzmann like dissipative equations; Granular gases; Long time behavior of solutions

Indexed keywords


EID: 3543013213     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:joss.0000013964.98706.00     Document Type: Article
Times cited : (48)

References (27)
  • 2
    • 84919348654 scopus 로고    scopus 로고
    • Multiscaling in inelastic collisions
    • N. Ben-Naim and P. Krapivski, Multiscaling in inelastic collisions, Phys. Rev. E 61: R5-R8 (2000).
    • (2000) Phys. Rev. E , vol.61
    • Ben-Naim, N.1    Krapivski, P.2
  • 3
    • 0000411415 scopus 로고
    • The theory of the nonlinear spatially uniform Boltzmann equation for Maxwellian molecules
    • A. V. Bobylev, The theory of the nonlinear spatially uniform Boltzmann equation for Maxwellian molecules, Sov. Sci. Rev. C 7:111-233 (1988).
    • (1988) Sov. Sci. Rev. C , vol.7 , pp. 111-233
    • Bobylev, A.V.1
  • 4
    • 0034343060 scopus 로고    scopus 로고
    • On some properties of kinetic and hydrodynamics equations for inelastic interactions
    • A. V. Bobylev, J. A. Carrillo, and I. Gamba, On some properties of kinetic and hydrodynamics equations for inelastic interactions, J. Stat. Phys. 98:743-773 (2000).
    • (2000) J. Stat. Phys. , vol.98 , pp. 743-773
    • Bobylev, A.V.1    Carrillo, J.A.2    Gamba, I.3
  • 5
    • 0036115583 scopus 로고    scopus 로고
    • Moment equation for a granular material in a thermal bath
    • A. V. Bobylev and C. Cercignani, Moment equation for a granular material in a thermal bath, J. Stat. Phys. 106:547-567 (2002).
    • (2002) J. Stat. Phys. , vol.106 , pp. 547-567
    • Bobylev, A.V.1    Cercignani, C.2
  • 6
    • 0036108114 scopus 로고    scopus 로고
    • Exact eternal solutions of the Boltzmann equation
    • A. V. Bobylev and C. Cercignani, Exact eternal solutions of the Boltzmann equation, J. Stat. Phys. 106:1019-1038 (2002).
    • (2002) J. Stat. Phys. , vol.106 , pp. 1019-1038
    • Bobylev, A.V.1    Cercignani, C.2
  • 7
    • 0036108115 scopus 로고    scopus 로고
    • Self-similar solutions of the Boltzmann equation and their applications
    • A. V. Bobylev and C. Cercignani, Self-similar solutions of the Boltzmann equation and their applications, J. Stat. Phys. 106:1039-1071 (2002).
    • (2002) J. Stat. Phys. , vol.106 , pp. 1039-1071
    • Bobylev, A.V.1    Cercignani, C.2
  • 8
    • 0037210439 scopus 로고    scopus 로고
    • Self-similar asymptotics for the Boltzmann equation with inelastic and elastic interactions
    • A. V. Bobylev and C. Cercignani, Self-similar asymptotics for the Boltzmann equation with inelastic and elastic interactions, J. Stat. Phys. 110:333-375 (2003).
    • (2003) J. Stat. Phys. , vol.110 , pp. 333-375
    • Bobylev, A.V.1    Cercignani, C.2
  • 9
    • 0037276633 scopus 로고    scopus 로고
    • Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials
    • A. V. Bobylev, C. Cercignani, and G. Toscani, Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials, J. Stat. Phys. 111: 403-417 (2003).
    • (2003) J. Stat. Phys. , vol.111 , pp. 403-417
    • Bobylev, A.V.1    Cercignani, C.2    Toscani, G.3
  • 10
    • 0033249563 scopus 로고    scopus 로고
    • Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous Maxwellian gas
    • E. A. Carlen, E. Gabetta, and G. Toscani, Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous Maxwellian gas, Comm. Math. Phys. 305:521-546 (1999).
    • (1999) Comm. Math. Phys. , vol.305 , pp. 521-546
    • Carlen, E.A.1    Gabetta, E.2    Toscani, G.3
  • 11
    • 0034424120 scopus 로고    scopus 로고
    • Central limit theorem for Maxwellian molecules and truncation of the Wild expansion
    • E. A. Carlen, M. C. Carvalho, and E. Gabetta, Central limit theorem for Maxwellian molecules and truncation of the Wild expansion, Comm. Pure Appl. Math. 53:370-397 (2000).
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 370-397
    • Carlen, E.A.1    Carvalho, M.C.2    Gabetta, E.3
  • 12
    • 0034504071 scopus 로고    scopus 로고
    • Steady states of a Boltzmann equation for driven granular media
    • J. A. Carrillo, C. Cercignani, and I. M. Gamba, Steady states of a Boltzmann equation for driven granular media, Phys. Rev. E 62:7700-7707 (2000).
    • (2000) Phys. Rev. E , vol.62 , pp. 7700-7707
    • Carrillo, J.A.1    Cercignani, C.2    Gamba, I.M.3
  • 13
    • 0035534231 scopus 로고    scopus 로고
    • Shear flow of a granular material
    • C. Cercignani, Shear flow of a granular material, J. Stat. Phys. 102:1407-1415 (2001).
    • (2001) J. Stat. Phys. , vol.102 , pp. 1407-1415
    • Cercignani, C.1
  • 15
    • 1642375713 scopus 로고    scopus 로고
    • High energy tails for inelastic Maxwell models
    • M. H. Ernst and R. Brito, High energy tails for inelastic Maxwell models, Europhys. Lett. 43:497-502 (2002).
    • (2002) Europhys. Lett. , vol.43 , pp. 497-502
    • Ernst, M.H.1    Brito, R.2
  • 16
    • 0036393182 scopus 로고    scopus 로고
    • Scaling solutions of inelastic Boltzmann equation with overpopulated high energy tails
    • M. H. Ernst and R. Brito, Scaling solutions of inelastic Boltzmann equation with overpopulated high energy tails, J. Stat. Phys. 109:407-432 (2002).
    • (2002) J. Stat. Phys. , vol.109 , pp. 407-432
    • Ernst, M.H.1    Brito, R.2
  • 17
    • 21844510511 scopus 로고
    • Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation
    • E. Gabetta, G. Toscani, and B. Wennberg, Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation, J. Stat. Phys. 81:901-934 (1995).
    • (1995) J. Stat. Phys. , vol.81 , pp. 901-934
    • Gabetta, E.1    Toscani, G.2    Wennberg, B.3
  • 18
    • 0036510434 scopus 로고    scopus 로고
    • Fourier-based distances and Berry-Esseen like inequalities for smooth densities
    • T. Goudon, S. Junca, and G. Toscani, Fourier-based distances and Berry-Esseen like inequalities for smooth densities, Monatsh. Math. 135:115-136 (2002).
    • (2002) Monatsh. Math. , vol.135 , pp. 115-136
    • Goudon, T.1    Junca, S.2    Toscani, G.3
  • 19
    • 0020811698 scopus 로고
    • Grain flow as a fluid-mechanical phenomenon
    • P. K. Haff, Grain flow as a fluid-mechanical phenomenon, J. Fluid Mech. 134:401-430 (1983).
    • (1983) J. Fluid Mech. , vol.134 , pp. 401-430
    • Haff, P.K.1
  • 24
    • 0001055303 scopus 로고
    • Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas
    • H. P. McKean, Jr., Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas, Arch. Rational Mech. Anal. 21:343-367 (1966).
    • (1966) Arch. Rational Mech. Anal. , vol.21 , pp. 343-367
    • McKean Jr., H.P.1
  • 25
    • 0034549474 scopus 로고    scopus 로고
    • One-dimensional kinetic models of granular flows
    • G. Toscani, One-dimensional kinetic models of granular flows, RAIRO Modél Math. Anal. Numér. 34:1277-1292 (2000).
    • (2000) RAIRO Modél Math. Anal. Numér. , vol.34 , pp. 1277-1292
    • Toscani, G.1
  • 26
    • 0033072701 scopus 로고    scopus 로고
    • Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas
    • G. Toscani and C. Villani, Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas, J. Stat. Phys. 94:619-637 (1999).
    • (1999) J. Stat. Phys. , vol.94 , pp. 619-637
    • Toscani, G.1    Villani, C.2
  • 27
    • 0033242961 scopus 로고    scopus 로고
    • Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation
    • G. Toscani and C. Villani, Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation, Comm. Math. Phys. 203:667-706 (1999).
    • (1999) Comm. Math. Phys. , vol.203 , pp. 667-706
    • Toscani, G.1    Villani, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.