메뉴 건너뛰기




Volumn 28, Issue 5, 1997, Pages 1015-1027

Boltzmann equation with infinite energy: Renormalized solutions and distributional solutions for small initial data and initial data close to a Maxwellian

Author keywords

Boltzmann equation; Dispersive effects; Distributional solution; Initial data close to a Maxwellian; Moments lemma; Renormalized solution; Small initial data

Indexed keywords


EID: 0031488084     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141096298102     Document Type: Article
Times cited : (42)

References (20)
  • 1
    • 84950042366 scopus 로고    scopus 로고
    • A priori estimates and existence results for the Vlasov and Boltzmann equations
    • Santa Fe, NM
    • C. BARDOS, P. DEGOND, AND F. GOLSE, A priori estimates and existence results for the Vlasov and Boltzmann equations, in Proc. 1984 AMS-SIAM Summer Seminar, Santa Fe, NM.
    • Proc. 1984 AMS-SIAM Summer Seminar
    • Bardos, C.1    Degond, P.2    Golse, F.3
  • 3
    • 0007219031 scopus 로고
    • On the Cauchy problem for the nonlinear Boltzmann equation. Global existence, uniqueness and asymptotic stability
    • N. BELLOMO AND G. TOSCANI, On the Cauchy problem for the nonlinear Boltzmann equation. Global existence, uniqueness and asymptotic stability, J. Math. Phys., 26 (1985), pp. 334-338.
    • (1985) J. Math. Phys. , vol.26 , pp. 334-338
    • Bellomo, N.1    Toscani, G.2
  • 5
  • 6
    • 0001089576 scopus 로고
    • On the Cauchy problem for Boltzmann equations: Global existence and weak stability
    • R. J. DIPERNA AND P-L. LIONS, On the Cauchy problem for Boltzmann equations: Global existence and weak stability, Ann. Math., 130 (1989), pp. 321-366.
    • (1989) Ann. Math. , vol.130 , pp. 321-366
    • Diperna, R.J.1    Lions, P.-L.2
  • 7
    • 0002627660 scopus 로고
    • Global solutions of Boltzmann equation and the entropy inequality
    • R. J. DIPERNA AND P-L. LIONS, Global solutions of Boltzmann equation and the entropy inequality, Arch. Rational Mech. Anal., 114 (1991), pp. 47-55.
    • (1991) Arch. Rational Mech. Anal. , vol.114 , pp. 47-55
    • Diperna, R.J.1    Lions, P.-L.2
  • 8
    • 45549114712 scopus 로고
    • Regularity of the moments of the solutions of a transport equation
    • F. GOLSE, P.-L. LIONS, B. PERTHAME, AND R. SENTIS, Regularity of the moments of the solutions of a transport equation, J. Functional Anal., 76 (1988), pp. 110-125.
    • (1988) J. Functional Anal. , vol.76 , pp. 110-125
    • Golse, F.1    Lions, P.-L.2    Perthame, B.3    Sentis, R.4
  • 9
    • 0001294845 scopus 로고
    • Principles of the kinetic theory of gases
    • H. GRAD, Principles of the kinetic theory of gases, Flügge's Handbuch der Physik, 12 (1958), pp. 205-294.
    • (1958) Flügge's Handbuch der Physik , vol.12 , pp. 205-294
    • Grad, H.1
  • 10
    • 0040943239 scopus 로고
    • The Boltzmann equation I: Uniqueness and global existence
    • S. KANIEL AND M. SHINBROT, The Boltzmann equation I: uniqueness and global existence, Comm. Math. Phys., 58 (1978), pp. 65-84.
    • (1978) Comm. Math. Phys. , vol.58 , pp. 65-84
    • Kaniel, S.1    Shinbrot, M.2
  • 11
    • 0007222794 scopus 로고
    • Existence in the large and asymptotic behaviour for the Boltzmann equation
    • K. HAMDACHE, Existence in the large and asymptotic behaviour for the Boltzmann equation, Japan J. Appl. Math., 2 (1985), pp. 1-15.
    • (1985) Japan J. Appl. Math. , vol.2 , pp. 1-15
    • Hamdache, K.1
  • 12
    • 0000638591 scopus 로고
    • Global existence for a rare gas in an infinite vacuum
    • R. ILLNER AND M. SHINBROT, Global existence for a rare gas in an infinite vacuum, Comm. Math. Phys., 95 (1984), pp. 117-126.
    • (1984) Comm. Math. Phys. , vol.95 , pp. 117-126
    • Illner, R.1    Shinbrot, M.2
  • 13
    • 0000834860 scopus 로고
    • Compactness in Boltzmann's equation via Fourier integral operators and applications. Parts I and II
    • P.-L. LIONS, Compactness in Boltzmann's equation via Fourier integral operators and applications. Parts I and II, J. Math. Kyoto Univ., 34 (1994), pp. 1-61.
    • (1994) J. Math. Kyoto Univ. , vol.34 , pp. 1-61
    • Lions, P.-L.1
  • 14
    • 0001255798 scopus 로고
    • Compactness in Boltzmann's equation via Fourier integral operators and applications. Part III
    • P.-L. LIONS, Compactness in Boltzmann's equation via Fourier integral operators and applications. Part III, J. Math. Kyoto Univ., 34 (1994), pp. 539-584.
    • (1994) J. Math. Kyoto Univ. , vol.34 , pp. 539-584
    • Lions, P.-L.1
  • 15
    • 0042249038 scopus 로고
    • Conditions at infinity for Boltzmann's equation
    • P.-L. LIONS, Conditions at infinity for Boltzmann's equation, Comm. Partial Differential Equations, 19 (1994), pp. 335-367.
    • (1994) Comm. Partial Differential Equations , vol.19 , pp. 335-367
    • Lions, P.-L.1
  • 16
    • 0000739837 scopus 로고
    • Lemmes de moments, de moyenne et de dispersion
    • P.-L. LIONS, B. PERTHAME, Lemmes de moments, de moyenne et de dispersion, C. R. Acad. Sci. Paris, 314 (1992), pp. 801-806.
    • (1992) C. R. Acad. Sci. Paris , vol.314 , pp. 801-806
    • Lions, P.-L.1    Perthame, B.2
  • 18
    • 0002288656 scopus 로고    scopus 로고
    • Time Decay, Propagation of Low Moments and Dispersive. Effects for Kinetic Equations
    • B. PERTHAME, Time Decay, Propagation of Low Moments and Dispersive. Effects for Kinetic Equations, Comm. Partial Differential Equations, 21 (1996), pp. 659-686.
    • (1996) Comm. Partial Differential Equations , vol.21 , pp. 659-686
    • Perthame, B.1
  • 19
    • 0002751118 scopus 로고
    • Global existence to the B.G.K. model of Boltzmann equation
    • B. PERTHAME, Global existence to the B.G.K. model of Boltzmann equation, J. Differential Equations, 82 (1989), pp. 191-205.
    • (1989) J. Differential Equations , vol.82 , pp. 191-205
    • Perthame, B.1
  • 20
    • 0007219529 scopus 로고
    • On the nonlinear Boltzmann equation in unbounded domains
    • G. TOSCANI, On the nonlinear Boltzmann equation in unbounded domains, Arch. Rational Mech. Anal., 95 (1986), pp. 37-49.
    • (1986) Arch. Rational Mech. Anal. , vol.95 , pp. 37-49
    • Toscani, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.