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Volumn 26, Issue 6, 1997, Pages 661-677

The generalized Boltzmann equation solution and exponential trend to equilibrium

Author keywords

Boltzmann equation; Equilibrium; Kinetic equations; Stability

Indexed keywords


EID: 0031323816     PISSN: 00411450     EISSN: None     Source Type: Journal    
DOI: 10.1080/00411459708229329     Document Type: Article
Times cited : (8)

References (32)
  • 1
    • 0000197530 scopus 로고
    • On the Boltzmann equation
    • L. Arkeryd, On the Boltzmann equation, Arch. Rat. Mech. Anal. 45 (1972), 1-34.
    • (1972) Arch. Rat. Mech. Anal. , vol.45 , pp. 1-34
    • Arkeryd, L.1
  • 2
    • 0000332895 scopus 로고
    • ∞ estimates for space-homogeneous Boltzmann equation
    • ∞ estimates for space-homogeneous Boltzmann equation, J. Statist. Phys., 31 (1983), 347-361.
    • (1983) J. Statist. Phys. , vol.31 , pp. 347-361
    • Arkeryd, L.1
  • 3
    • 0000224209 scopus 로고
    • 1 for the spatially homogeneous Boltzmann equation
    • 1 for the spatially homogeneous Boltzmann equation, Arch. Rat. Mech. Anal., 103 (1988), 151-167.
    • (1988) Arch. Rat. Mech. Anal. , vol.103 , pp. 151-167
    • Arkeryd, L.1
  • 4
    • 0012987026 scopus 로고
    • On the Enskog equation with large initial data
    • L. Arkeryd, On the Enskog equation with large initial data, SIAM J. Math. Anal, 21 (1990), 631-646.
    • (1990) SIAM J. Math. Anal , vol.21 , pp. 631-646
    • Arkeryd, L.1
  • 5
    • 0001288465 scopus 로고
    • 1 for the Enskog equation and convergence of solutions to solutions of the Boltzmann equation
    • 1 for the Enskog equation and convergence of solutions to solutions of the Boltzmann equation, J. Statist. Phys, 59 (1990), 845-867.
    • (1990) J. Statist. Phys , vol.59 , pp. 845-867
    • Arkeryd, L.1    Cercignani, C.2
  • 6
    • 84943150390 scopus 로고
    • 1 trend to equilibrium for the Boltzmann equation
    • 1 trend to equilibrium for the Boltzmann equation, Studies Appl. Math, 87 (1992), 282-283.
    • (1992) Studies Appl. Math , vol.87 , pp. 282-283
    • Arkeryd, L.1
  • 7
    • 0040204813 scopus 로고
    • Some examples of NSA methods in kinetic theory
    • Nonequilibrium Problems in Many-Particles Systems, Springer Verlag
    • L. Arkeryd, Some examples of NSA methods in kinetic theory, in Nonequilibrium Problems in Many-Particles Systems, Springer Lect. Notes in Math. n. 1551, Springer Verlag, (1993), 14-57.
    • (1993) Springer Lect. Notes in Math. , Issue.1551 , pp. 14-57
    • Arkeryd, L.1
  • 12
    • 0002931582 scopus 로고
    • Convergence to equilibrium in the large time for Boltzmann and BGK equations
    • L. Desvillettes, Convergence to equilibrium in the large time for Boltzmann and BGK equations, Arch. Rat. Mech. Anal. 11 (1990), 73-91.
    • (1990) Arch. Rat. Mech. Anal. , vol.11 , pp. 73-91
    • Desvillettes, L.1
  • 13
    • 0001089576 scopus 로고
    • On the Gauchy problem for the Boltzmann equation: Global existence and weak stability
    • R. DiPerna and P. L. Lions, On the Gauchy problem for the Boltzmann equation: Global existence and weak stability, Annals of Mathematics, 130 (1989), 321-366.
    • (1989) Annals of Mathematics , vol.130 , pp. 321-366
    • DiPerna, R.1    Lions, P.L.2
  • 14
    • 0002627660 scopus 로고
    • Global solutions of the Boltzmann equation and entropy inequality
    • R. DiPerna and P. L. Lions, Global solutions of the Boltzmann equation and entropy inequality, Arch. Rat. Mech. Anal. 114 (1991), 47-55.
    • (1991) Arch. Rat. Mech. Anal. , vol.114 , pp. 47-55
    • DiPerna, R.1    Lions, P.L.2
  • 15
    • 0020633583 scopus 로고
    • Global boundedness of moments of solutions of the Boltzmann equation for forces of infinite range
    • T. Elmroth, Global boundedness of moments of solutions of the Boltzmann equation for forces of infinite range, Arch. Rat. Mech. Anal., 82 (1983), 1-12.
    • (1983) Arch. Rat. Mech. Anal. , vol.82 , pp. 1-12
    • Elmroth, T.1
  • 16
    • 0040799091 scopus 로고
    • On the H-function and convergence towards equilibrium for a space homogeneous molecular density
    • T. Elmroth, On the H-function and convergence towards equilibrium for a space homogeneous molecular density, SIAM. J. Appl. Math., 44 (1984), 150-159.
    • (1984) SIAM. J. Appl. Math. , vol.44 , pp. 150-159
    • Elmroth, T.1
  • 17
    • 0040204825 scopus 로고
    • Global solutions for the modified Enskog equation with elastic and inelastic collisions
    • M. J. Esteban and B. Pertharne, Global solutions for the modified Enskog equation with elastic and inelastic collisions, C.R. Acad. Sc. Paris, Série I, 309 (1989), 897-902.
    • (1989) C.R. Acad. Sc. Paris, Série I , vol.309 , pp. 897-902
    • Esteban, M.J.1    Pertharne, B.2
  • 18
    • 84864161175 scopus 로고
    • On the modified Enskog equation for elastic and inelastic collisions. Models with spin
    • M. J. Esteban and B. Pertharne, On the modified Enskog equation for elastic and inelastic collisions. Models with spin, Ann. Inst. Poincare, 8 (1991), 289-308.
    • (1991) Ann. Inst. Poincare , vol.8 , pp. 289-308
    • Esteban, M.J.1    Pertharne, B.2
  • 19
    • 0002325091 scopus 로고
    • p-estimates for the nonlinear spatially homogenous Boltzmann equation
    • p-Estimates for the nonlinear spatially homogenous Boltzmann equation, Arch. Rat. Mech. Anal., 92 (1986), 23-57.
    • (1986) Arch. Rat. Mech. Anal. , vol.92 , pp. 23-57
    • Gustafsson, T.1
  • 20
    • 0002412857 scopus 로고
    • p-properties for the spatially homogeneous Boltzmann equation
    • p-Properties for the spatially homogeneous Boltzmann equation, Arch. Rat. Mech. Anal., 103 (1988), 1-38.
    • (1988) Arch. Rat. Mech. Anal. , vol.103 , pp. 1-38
    • Gustafsson, T.1
  • 21
    • 0025567374 scopus 로고
    • A stochastic system of particles modelling the Euler equations
    • M. Lachowicz and M. Pulvirenti, A Stochastic system of Particles Modelling the Euler Equations, Arch. Rat. Mech. Anal., 109 (1990), 81-93.
    • (1990) Arch. Rat. Mech. Anal. , vol.109 , pp. 81-93
    • Lachowicz, M.1    Pulvirenti, M.2
  • 22
    • 0000834860 scopus 로고
    • Compactness in Boltzmann equation via Fourier integrals operator and applications I
    • P.L. Lions, Compactness in Boltzmann equation via Fourier integrals operator and applications I, J. Math. Kyoto Univ., 34 (1994) 391-427.
    • (1994) J. Math. Kyoto Univ. , vol.34 , pp. 391-427
    • Lions, P.L.1
  • 23
    • 0000834860 scopus 로고
    • Compactness in Boltzmann equation via Fourier integrals operator and applications II
    • P.L. Lions, Compactness in Boltzmann equation via Fourier integrals operator and applications II, J. Math. Kyoto Univ., 34 (1994) 429-461.
    • (1994) J. Math. Kyoto Univ. , vol.34 , pp. 429-461
    • Lions, P.L.1
  • 24
    • 0005525165 scopus 로고
    • Analytic studies related to the Maxwell Boltzmann equation
    • D. Morgenstern, Analytic studies related to the Maxwell Boltzmann equation, Arch. Rat. Mech. Anal., 4 (1955), 535-555.
    • (1955) Arch. Rat. Mech. Anal. , vol.4 , pp. 535-555
    • Morgenstern, D.1
  • 25
    • 0002136787 scopus 로고
    • 1 for the generalized Enskog equation
    • 1 for the generalized Enskog equation, J. Statist. Phys, 59 (1990), 461-500.
    • (1990) J. Statist. Phys , vol.59 , pp. 461-500
    • Polewczak, J.1
  • 26
    • 0002020598 scopus 로고
    • New properties of a class of generalized kinetic equations
    • J. Polewczak and G. Stell, New properties of a class of generalized kinetic equations, J. Statist. Phys, 64 (1991), 437-464.
    • (1991) J. Statist. Phys , vol.64 , pp. 437-464
    • Polewczak, J.1    Stell, G.2
  • 27
    • 0011368669 scopus 로고
    • About the Boltzmann equation in kinetic gas theory
    • A. J. Povzner, About the Boltzmann equation in kinetic gas theory, Math. SSSR Sb., 58 (1962), 65-86.
    • (1962) Math. SSSR Sb. , vol.58 , pp. 65-86
    • Povzner, A.J.1
  • 28
    • 5644232645 scopus 로고
    • H-theorem for the (modified) nonlinear Enskog equation
    • P. Résibois, H-theorem for the (modified) nonlinear Enskog equation, J. Statist. Phys, 19 (1978), 593-609.
    • (1978) J. Statist. Phys , vol.19 , pp. 593-609
    • Résibois, P.1
  • 31
    • 85033116085 scopus 로고    scopus 로고
    • Personal Communication
    • B. Wennberg, Personal Communication.
    • Wennberg, B.1
  • 32
    • 0001210972 scopus 로고
    • Regularity in the Boltzmann equation and the Radon transform
    • B. Wennberg, Regularity in the Boltzmann equation and the Radon Transform, Comm. Partial Diff. Equations, 19 (1994), 2057-2074.
    • (1994) Comm. Partial Diff. Equations , vol.19 , pp. 2057-2074
    • Wennberg, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.