메뉴 건너뛰기




Volumn 24, Issue 1, 2009, Pages 13-33

Propagation of singularities for classical solutions of the Vlasov-Poisson-Boltzmann equation

Author keywords

Averaging Lemma; Boltzmann Equation; Propagation of Singularities; Vlasov Equation

Indexed keywords


EID: 67349191211     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2009.24.13     Document Type: Article
Times cited : (7)

References (22)
  • 1
    • 67449151602 scopus 로고    scopus 로고
    • PhD Thesis, University of Orléans
    • L. Bernis, "PhD Thesis," University of Orléans, 2006.
    • (2006)
    • Bernis, L.1
  • 3
    • 0032220965 scopus 로고    scopus 로고
    • A proof of the smoothing properties of the positive part of Boltzmann's kernel
    • F. Bouchut and L. Desvillettes, A proof of the smoothing properties of the positive part of Boltzmann's kernel, Rev. Mat. Iberoamericana, 14 (1998), 47-61.
    • (1998) Rev. Mat. Iberoamericana , vol.14 , pp. 47-61
    • Bouchut, F.1    Desvillettes, L.2
  • 4
    • 0003840403 scopus 로고    scopus 로고
    • On the singularities of the global small solutions of the full Boltzmann equation system
    • L. Boudin and L. Desvillettes, On the singularities of the global small solutions of the full Boltzmann equation system, Monatsch. Math., 131 (2000), 91-108.
    • (2000) Monatsch. Math , vol.131 , pp. 91-108
    • Boudin, L.1    Desvillettes, L.2
  • 7
    • 67449126225 scopus 로고    scopus 로고
    • Smoothness of classical solutions to the Vlasov-Poisson- Landau system near Maxwellians
    • Preprint
    • Y. Chen, Smoothness of classical solutions to the Vlasov-Poisson- Landau system near Maxwellians, Preprint.
    • Chen, Y.1
  • 8
    • 44849101217 scopus 로고    scopus 로고
    • Smoothness of classical solutions to the Vlasov-Maxwell- Landau system near Maxwellians
    • Y. Chen, Smoothness of classical solutions to the Vlasov-Maxwell- Landau system near Maxwellians, Discrete Contin. Dyn. Syst., 20 (2008), 91-108.
    • (2008) Discrete Contin. Dyn. Syst , vol.20 , pp. 91-108
    • Chen, Y.1
  • 10
    • 0000195197 scopus 로고
    • On long time asymptotics of the Vlasov-Poisson-Boltzmann equation
    • L. Desvillettes and J. Dolbeault, On long time asymptotics of the Vlasov-Poisson-Boltzmann equation, Comm. Partial Differential Equations, 16 (1991), 451-489.
    • (1991) Comm. Partial Differential Equations , vol.16 , pp. 451-489
    • Desvillettes, L.1    Dolbeault, J.2
  • 11
    • 84990553444 scopus 로고
    • Global weak solutions of Vlasov-Maxwell systems
    • R. J. Di Perna and P.-L. Lions, Global weak solutions of Vlasov-Maxwell systems, Comm. Pure Appl. Math., 42 (1989), 729-757.
    • (1989) Comm. Pure Appl. Math , vol.42 , pp. 729-757
    • Di Perna, R.J.1    Lions, P.-L.2
  • 12
    • 33747711299 scopus 로고    scopus 로고
    • Boltzmann equation whith external force and Vlasov-Poisson-Boltzmann system in infinite vacuum
    • R. J. Duan, T. Yang and C. J. Zhu, Boltzmann equation whith external force and Vlasov-Poisson-Boltzmann system in infinite vacuum, Discrete and Continuous Dynamical Systems, 16 (2006), 253-277.
    • (2006) Discrete and Continuous Dynamical Systems , vol.16 , pp. 253-277
    • Duan, R.J.1    Yang, T.2    Zhu, C.J.3
  • 13
    • 45549114712 scopus 로고
    • Regularity of the moments of the solution of a transport equation
    • F. Golse, P.-L. Lions, B. Perthame and R. Sentis, Regularity of the moments of the solution of a transport equation, J. Funct. Anal., 76 (1988), 110-125.
    • (1988) J. Funct. Anal , vol.76 , pp. 110-125
    • Golse, F.1    Lions, P.-L.2    Perthame, B.3    Sentis, R.4
  • 14
    • 0000053323 scopus 로고
    • Un résulted de compacité pour les équations de transport et application au calcul de la limite de la valeur propre principale d 'un opérateur de transport
    • Série I
    • F. Golse, B. Perthame and R. Sentis, Un résulted de compacité pour les équations de transport et application au calcul de la limite de la valeur propre principale d 'un opérateur de transport, C. R. Acad. Sc, Série I, 301 (1985), 341-344.
    • (1985) C. R. Acad. Sc , vol.301 , pp. 341-344
    • Golse, F.1    Perthame, B.2    Sentis, R.3
  • 15
    • 0036328887 scopus 로고    scopus 로고
    • The Vlasov-Poisson-Boltzmann system near Maxwellians
    • Y. Guo, The Vlasov-Poisson-Boltzmann system near Maxwellians, Comm. Pure Appl. Math., 55 (2002), 1104-1135.
    • (2002) Comm. Pure Appl. Math , vol.55 , pp. 1104-1135
    • Guo, Y.1
  • 16
    • 0035531905 scopus 로고    scopus 로고
    • The Vlasov-Poisson-Boltzmann system near vacuum
    • Y. Guo, The Vlasov-Poisson-Boltzmann system near vacuum, Comm. Math. Phys., 218 (2001), 293-313.
    • (2001) Comm. Math. Phys , vol.218 , pp. 293-313
    • Guo, Y.1
  • 17
    • 42649130013 scopus 로고    scopus 로고
    • Regularities of the solutions to the Fokker-Planck-Boltzmann equation
    • L. He, Regularities of the solutions to the Fokker-Planck-Boltzmann equation, J. Differential Equations, 244 (2008), 3060-3079.
    • (2008) J. Differential Equations , vol.244 , pp. 3060-3079
    • He, L.1
  • 19
    • 0000834860 scopus 로고
    • Compactness in Boltzmann equation via Fourier integral operators and applications, I
    • P.-L. Lions, Compactness in Boltzmann equation via Fourier integral operators 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
  • 20
    • 0001255798 scopus 로고
    • Compactness in Boltzmann equation via Fourier integral operators and applications, III
    • P.-L. Lions, Compactness in Boltzmann equation via Fourier integral operators and applications, III, J. Math. Kyoto Univ., 34 (1994), 539-584.
    • (1994) J. Math. Kyoto Univ , vol.34 , pp. 539-584
    • Lions, P.-L.1
  • 21
    • 0038161745 scopus 로고    scopus 로고
    • A direct method for the regularity of the gain term in the Boltzmann equation
    • X. Lu, A direct method for the regularity of the gain term in the Boltzmann equation, J. Math. Anal. Appl., 228 (1998), 409-435.
    • (1998) J. Math. Anal. Appl , vol.228 , pp. 409-435
    • Lu, X.1
  • 22
    • 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 Differential Equations, 19 (1994), 2057-2074.
    • (1994) Comm. Partial Differential Equations , vol.19 , pp. 2057-2074
    • Wennberg, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.