본문 바로가기
HOME> 논문 > 논문 검색상세

논문 상세정보

Journal of the Korean Mathematical Society = 대한수학회지 v.47 no.4, 2010년, pp.743 - 766   SCIE SCOPUS
본 등재정보는 저널의 등재정보를 참고하여 보여주는 베타서비스로 정확한 논문의 등재여부는 등재기관에 확인하시기 바랍니다.

BOUNDARY VALUE PROBLEMS FOR THE STATIONARY NORDSTROM-VLASOV SYSTEM

Bostan, Mihai    (LABORATOIRE DE MATHEMATIQUES DE BESANCON UMR CNRS 6623, UNIVERSITE DE FRANCHE-COMTE  );
  • 초록

    We study the existence of weak solution for the stationary Nordstr $\ddot{o}$ m-Vlasov equations in a bounded domain. The proof follows by fixed point method. The asymptotic behavior for large light speed is analyzed as well. We justify the convergence towards the stationary Vlasov-Poisson model for stellar dynamics.


  • 주제어

    Nordstr $\ddot{o}$m equation .   Vlasov equation .   Poisson equation .   weak/mild solutions.  

  • 참고문헌 (39)

    1. N. B. Abdallah, Weak solutions of the initial-boundary value problem for the Vlasov-Poisson system, Math. Methods Appl. Sci. 17 (1994), no. 6, 451-476. 
    2. H. Andreasson, The Einstein-Vlasov system/kinetic theory, Living Rev. Relativ. 5 (2002), 2002-7, 33 pp. 
    3. A. Arsen'ev, Global existence of a weak solution of the Vlasov system of equations, U.R.S.S. Comp. and Math. Phys. 15 (1975), 131-143. 
    4. C. Bardos, Problemes aux limites pour les equations aux derivees partielles du premier ordre a coefficients reels; theoremes d'approximation; application a l'equation de transport, Ann. Sci. Ecole Norm. Sup. (4) 3 (1970), 185-233. 
    5. J. Batt, W. Faltenbacher, and E. Horst, Stationary spherically symmetric models in stellar dynamics, Arch. Rational Mech. Anal. 93 (1986), no. 2, 159-183. 
    6. J. Batt, P. Morrison, and G. Rein, Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions, Arch. Rational Mech. Anal. 130 (1995), no. 2, 163-182. 
    7. M. Bostan, Boundary value problem for the three dimensional time periodic Vlasov-Maxwell system, Commun. Math. Sci. 3 (2005), no. 4, 621-663. 
    8. M. Bostan, Asymptotic behavior of weak solutions for the relativistic Vlasov-Maxwell equations with large light speed, J. Differential Equations 227 (2006), no. 2, 444-498. 
    9. M. Bostan, Stationary solutions for the one dimensional Nordstrom-Vlasov system, Preprint 22 (2006), Universite de Franche-Comte. 
    10. F. Bouchut, F. Golse, and C. Pallard, Classical solutions and the Glassey-Strauss theorem for the 3D Vlasov-Maxwell system, Arch. Ration. Mech. Anal. 170 (2003), no. 1, 1-15. 
    11. S. Calogero, Spherically symmetric steady states of galactic dynamics in scalar gravity, Classical Quantum Gravity 20 (2003), no. 9, 1729?1741. 
    12. S. Calogero and H. Lee, The non-relativistic limit of the Nordstrom-Vlasov system, Commun. Math. Sci. 2 (2004), no. 1, 19-34. 
    13. S. Calogero and G. Rein, On classical solutions of the Nordstrom-Vlasov system, Comm. Partial Differential Equations 28 (2003), no. 11-12, 1863-1885. 
    14. S. Calogero and G. Rein, Global weak solutions to the Nordstrom-Vlasov system, J. Differential Equations 204 (2004), no. 2, 323-338. 
    15. P. Degond, Local existence of solutions of the Vlasov-Maxwell equations and convergence to the Vlasov-Poisson equations for infinite light velocity, Math. Methods Appl. Sci. 8 (1986), no. 4, 533-558. 
    16. R. J. Diperna and P.-L. Lions, Global weak solutions of Vlasov-Maxwell systems, Comm. Pure Appl. Math. 42 (1989), no. 6, 729-757. 
    17. R. J. Diperna and P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989), no. 3, 511-547. 
    18. J. Dolbeault, O. Sanchez, and J. Soler, Asymptotic behaviour for the Vlasov-Poisson system in the stellar-dynamics case, Arch. Ration. Mech. Anal. 171 (2004), no. 3, 301-327. 
    19. R. Glassey and J. Schaeffer, On the “one and one-half dimensional” relativistic Vlasov-Maxwell system, Math. Methods Appl. Sci. 13 (1990), no. 2, 169-179. 
    20. R. Glassey and J. Schaeffer, The “two and one-half-dimensional” relativistic Vlasov Maxwell system, Comm. Math. Phys. 185 (1997), no. 2, 257-284. 
    21. R. Glassey and W. Strauss, Singularity formation in a collisionless plasma could occur only at high velocities, Arch. Rational Mech. Anal. 92 (1986), no. 1, 59-90. 
    22. C. Greengard and P.-A. Raviart, A boundary-value problem for the stationary Vlasov-Poisson equations: the plane diode, Comm. Pure Appl. Math. 43 (1990), no. 4, 473-507. 
    23. Y. Guo, Global weak solutions of the Vlasov-Maxwell system with boundary conditions, Comm. Math. Phys. 154 (1993), no. 2, 245-263. 
    24. S. Klainerman and G. Staffilani, A new approach to study the Vlasov-Maxwell system, Commun. Pure Appl. Anal. 1 (2002), no. 1, 103-125. 
    25. H. Lee, The classical limit of the relativistic Vlasov-Maxwell system in two space dimensions, Math. Methods Appl. Sci. 27 (2004), no. 3, 249-287. 
    26. P.-L. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math. 105 (1991), no. 2, 415-430. 
    27. S. Mischler, On the trace problem for solutions of the Vlasov equation, Comm. Partial Differential Equations 25 (2000), no. 7-8, 1415-1443. 
    28. G. Nordstrom, Zur Theorie der Gravitation vom Standpunkt des Relativitatsprinzips, Ann. Phys. 347 (1913), no. 13, 533-554. 
    29. F. Poupaud, Boundary value problems for the stationary Vlasov-Maxwell system, Forum Math. 4 (1992), no. 5, 499-527. 
    30. K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Differential Equations 95 (1992), no. 2, 281-303. 
    31. G. Rein, Existence of stationary, collisionless plasmas in bounded domains, Math. Methods Appl. Sci. 15 (1992), no. 5, 365-374. 
    32. G. Rein, Non-linear stability for the Vlasov-Poisson system-the energy-Casimir method, Math. Methods Appl. Sci. 17 (1994), no. 14, 1129-1140. 
    33. G. Rein, Selfgravitating systems in Newtonian theory-the Vlasov-Poisson system, Mathematics of gravitation, Part I (Warsaw, 1996), 179-194, Banach Center Publ., 41, Part I, Polish Acad. Sci., Warsaw, 1997. 
    34. G. Rein, Stationary and static stellar dynamic models with axial symmetry, Nonlinear Anal. 41 (2000), no. 3-4, Ser. A: Theory Methods, 313-344. 
    35. G. Rein and A. D. Rendall, Global existence of classical solutions to the Vlasov-Poisson system in a three-dimensional, cosmological setting, Arch. Rational Mech. Anal. 126 (1994), no. 2, 183-201. 
    36. A. D. Rendall, An introduction to the Einstein-Vlasov system, Mathematics of gravitation, Part I (Warsaw, 1996), 35-68, Banach Center Publ., 41, Part I, Polish Acad. Sci., Warsaw, 1997. 
    37. A. D. Rendall, The Einstein-Vlasov system, The Einstein equations and the large scale behavior of gravitational fields, 231-250, Birkhauser, Basel, 2004. 
    38. J. Schaeffer, The classical limit of the relativistic Vlasov-Maxwell system, Comm. Math. Phys. 104 (1986), no. 3, 403-421. 
    39. J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Comm. Partial Differential Equations 16 (1991), no. 8-9, 1313-1335. 

 활용도 분석

  • 상세보기

    amChart 영역
  • 원문보기

    amChart 영역

원문보기

무료다운로드
유료다운로드
  • 원문이 없습니다.

유료 다운로드의 경우 해당 사이트의 정책에 따라 신규 회원가입, 로그인, 유료 구매 등이 필요할 수 있습니다. 해당 사이트에서 발생하는 귀하의 모든 정보활동은 NDSL의 서비스 정책과 무관합니다.

원문복사신청을 하시면, 일부 해외 인쇄학술지의 경우 외국학술지지원센터(FRIC)에서
무료 원문복사 서비스를 제공합니다.

NDSL에서는 해당 원문을 복사서비스하고 있습니다. 위의 원문복사신청 또는 장바구니 담기를 통하여 원문복사서비스 이용이 가능합니다.

이 논문과 함께 출판된 논문 + 더보기