메뉴 건너뛰기




Volumn 4, Issue 4, 2011, Pages 873-900

Fractional diffusion limit for collisional kinetic equations: A Hilbert expansion approach

Author keywords

Anomalous diffusion limit; Fractional diffusion; Linear Boltzmann equation

Indexed keywords


EID: 84856264748     PISSN: 19375093     EISSN: 19375077     Source Type: Journal    
DOI: 10.3934/krm.2011.4.873     Document Type: Article
Times cited : (39)

References (17)
  • 1
    • 84967735805 scopus 로고
    • Diffusion approximation and computation of the critical size
    • C. Bardos, R. Santos and R. Sentis, Diffusion approximation and computation of the critical size, Trans. A. M. S., 284 (1984), 617-649.
    • (1984) Trans. A. M. S. , vol.284 , pp. 617-649
    • Bardos, C.1    Santos, R.2    Sentis, R.3
  • 2
    • 0030537690 scopus 로고    scopus 로고
    • On a hierarchy of macroscopic models for semiconductors
    • N. Ben Abdallah and P. Degond, On a hierarchy of macroscopic models for semiconductors, J. Math. Phys., 37 (1996), 3306-3333.
    • (1996) J. Math. Phys. , vol.37 , pp. 3306-3333
    • Ben Abdallah, N.1    Degond, P.2
  • 3
    • 84856271206 scopus 로고    scopus 로고
    • Anomalous diffusion limit for kinetic equations with degenerate collision frequency
    • to appear
    • N. Ben Abdallah, A. Mellet and M. Puel, Anomalous diffusion limit for kinetic equations with degenerate collision frequency, Math. Models Methods Appl. Sci., to appear.
    • Math. Models Methods Appl. Sci.
    • Ben Abdallah, N.1    Mellet, A.2    Puel, M.3
  • 5
    • 0034343060 scopus 로고    scopus 로고
    • On some properties of kinetic and hydrodynamic equations for inelastic interactions
    • A. V. Bobylev, J. A. Carrillo and I. M. Gamba, On some properties of kinetic and hydrodynamic equations for inelastic interactions, J. Statist. Phys., 98 (2000), 743-773.
    • (2000) J. Statist. Phys. , vol.98 , pp. 743-773
    • Bobylev, A.V.1    Carrillo, J.A.2    Gamba, I.M.3
  • 6
    • 33751038059 scopus 로고    scopus 로고
    • Boltzmann equations for mixtures of Maxwell gases: Exact solutions and power like tails
    • A. V. Bobylev and I. M. Gamba, Boltzmann equations for mixtures of Maxwell gases: Exact solutions and power like tails, J. Stat. Phys., 124 (2006), 497-516.
    • (2006) J. Stat. Phys. , vol.124 , pp. 497-516
    • Bobylev, A.V.1    Gamba, I.M.2
  • 7
    • 0000512903 scopus 로고    scopus 로고
    • Diffusion limit for nonhomogeneous and non-micro-reversibles processes
    • P. Degond, T. Goudon and F. Poupaud, Diffusion limit for nonhomogeneous and non-micro-reversibles processes, Indiana Univ. Math. J., 49 (2000), 1175-1198.
    • (2000) Indiana Univ. Math. J. , vol.49 , pp. 1175-1198
    • Degond, P.1    Goudon, T.2    Poupaud, F.3
  • 8
    • 0036393182 scopus 로고    scopus 로고
    • Scaling solutions of inelastic Boltzmann equations with over-populated high energy tails
    • M. H. Ernst and R. Brito, Scaling solutions of inelastic Boltzmann equations with over-populated high energy tails, J. Statist. Phys., 109 (2002), 407-432.
    • (2002) J. Statist. Phys. , vol.109 , pp. 407-432
    • Ernst, M.H.1    Brito, R.2
  • 9
    • 0037457054 scopus 로고    scopus 로고
    • On fluid limit for the semiconductors Boltzmann equation
    • T. Goudon and A. Mellet, On fluid limit for the semiconductors Boltzmann equation, Journal Diff. Equations, 189 (2003), 17-45.
    • (2003) Journal Diff. Equations , vol.189 , pp. 17-45
    • Goudon, T.1    Mellet, A.2
  • 10
    • 36849113737 scopus 로고
    • Asymptotic solution of neutron transport problems for small mean free paths
    • E. W. Larsen and J. B. Keller, Asymptotic solution of neutron transport problems for small mean free paths, J. Math. Phys., 15 (1974), 75-81.
    • (1974) J. Math. Phys. , vol.15 , pp. 75-81
    • Larsen, E.W.1    Keller, J.B.2
  • 11
    • 77953625018 scopus 로고    scopus 로고
    • On the diffusion limit of a semiconductor Boltzmann-Poisson system without micro-reversible process
    • N. Masmoudi and M.-L. Tayeb, On the diffusion limit of a semiconductor Boltzmann-Poisson system without micro-reversible process, Comm. Partial Differential Equations, 35 (2010), 1163-1175.
    • (2010) Comm. Partial Differential Equations , vol.35 , pp. 1163-1175
    • Masmoudi, N.1    Tayeb, M.-L.2
  • 12
    • 0012862895 scopus 로고    scopus 로고
    • Diffusion limit of a nonlinear kinetic model without the detailed balance principle
    • A. Mellet Diffusion limit of a nonlinear kinetic model without the detailed balance principle, Monatshefte f. Mathematik, 134 (2002), 305-329.
    • (2002) Monatshefte f. Mathematik , vol.134 , pp. 305-329
    • Mellet, A.1
  • 13
    • 79954442335 scopus 로고    scopus 로고
    • Fractional diffusion limit for collisional kinetic equations: A moments method
    • A. Mellet, Fractional diffusion limit for collisional kinetic equations: A moments method, Indiana Univ. Math. J., 59 (2010), 1333-1360.
    • (2010) Indiana Univ. Math. J. , vol.59 , pp. 1333-1360
    • Mellet, A.1
  • 14
    • 78751650015 scopus 로고    scopus 로고
    • Fractional diffusion limit for collisional kinetic equations
    • A. Mellet, S. Mischler and C. Mouhot, Fractional diffusion limit for collisional kinetic equations, Arch. Ration. Mech. Anal., 199 (2011), 493-525.
    • (2011) Arch. Ration. Mech. Anal. , vol.199 , pp. 493-525
    • Mellet, A.1    Mischler, S.2    Mouhot, C.3
  • 16
    • 3543013213 scopus 로고    scopus 로고
    • Asymptotic properties of the inelastic Kac model
    • A. Pulvirenti and G. Toscani, Asymptotic properties of the inelastic Kac model, J. Statist. Phys., 114 (2004), 1453-1480.
    • (2004) J. Statist. Phys. , vol.114 , pp. 1453-1480
    • Pulvirenti, A.1    Toscani, G.2
  • 17
    • 0000684006 scopus 로고
    • The modified plasma dispersion function
    • D. Summers and R. M. Thorne, The modified plasma dispersion function, Phys. Fluids, 83 (1991), 1835-1847.
    • (1991) Phys. Fluids , vol.83 , pp. 1835-1847
    • Summers, D.1    Thorne, R.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.