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      KCI등재 SCIE SCOPUS

      BOUNDARY VALUE PROBLEMS FOR THE STATIONARY NORDSTR¨OM-VLASOV SYSTEM

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      https://www.riss.kr/link?id=A103365701

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      다국어 초록 (Multilingual Abstract)

      We study the existence of weak solution for the stationary Nordstr¨om-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...

      We study the existence of weak solution for the stationary Nordstr¨om-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.

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      참고문헌 (Reference)

      1 R. Glassey, "“two and one-half-dimensional” relativistic Vlasov Maxwell system" 185 (185): 257-284, 1997

      2 G. Nordstr¨om, "Zur Theorie der Gravitation vom Standpunkt des Relativit¨atsprinzips" 347 (347): 533-554, 1913

      3 N. B. Abdallah, "Weak solutions of the initial-boundary value problem for the Vlasov-Poisson system" 17 (17): 451-476, 1994

      4 S. Calogero, "The non-relativistic limit of the Nordstr¨om-Vlasov system" 2 (2): 19-34, 2004

      5 H. Lee, "The classical limit of the relativistic Vlasov-Maxwell system in two space dimensions" 27 (27): 249-287, 2004

      6 J. Schaeffer, "The classical limit of the relativistic Vlasov-Maxwell system" 104 (104): 403-421, 1986

      7 H. Andr´easson, "The Einstein-Vlasov system/kinetic theory" 5 : 33-, 2002

      8 A. D. Rendall, "The Einstein-Vlasov system, The Einstein equations and the large scale behavior of gravitational fields" Birkhauser 231-250, 2004

      9 J. Batt, "Stationary spherically symmetric models in stellar dynamics" 93 (93): 159-183, 1986

      10 M. Bostan, "Stationary solutions for the one dimensional Nordstr¨om-Vlasov system, Preprint 22" Universit´e de Franche-Comt´e 2006

      1 R. Glassey, "“two and one-half-dimensional” relativistic Vlasov Maxwell system" 185 (185): 257-284, 1997

      2 G. Nordstr¨om, "Zur Theorie der Gravitation vom Standpunkt des Relativit¨atsprinzips" 347 (347): 533-554, 1913

      3 N. B. Abdallah, "Weak solutions of the initial-boundary value problem for the Vlasov-Poisson system" 17 (17): 451-476, 1994

      4 S. Calogero, "The non-relativistic limit of the Nordstr¨om-Vlasov system" 2 (2): 19-34, 2004

      5 H. Lee, "The classical limit of the relativistic Vlasov-Maxwell system in two space dimensions" 27 (27): 249-287, 2004

      6 J. Schaeffer, "The classical limit of the relativistic Vlasov-Maxwell system" 104 (104): 403-421, 1986

      7 H. Andr´easson, "The Einstein-Vlasov system/kinetic theory" 5 : 33-, 2002

      8 A. D. Rendall, "The Einstein-Vlasov system, The Einstein equations and the large scale behavior of gravitational fields" Birkhauser 231-250, 2004

      9 J. Batt, "Stationary spherically symmetric models in stellar dynamics" 93 (93): 159-183, 1986

      10 M. Bostan, "Stationary solutions for the one dimensional Nordstr¨om-Vlasov system, Preprint 22" Universit´e de Franche-Comt´e 2006

      11 G. Rein, "Stationary and static stellar dynamic models with axial symmetry" Ser. A: Theory Methods 41 (41): 313-344, 2000

      12 S. Calogero, "Spherically symmetric steady states of galactic dynamics in scalar gravity" 20 (20): 1729-1741, 2003

      13 R. Glassey, "Singularity formation in a collisionless plasma could occur only at high velocities" 92 (92): 59-90, 1986

      14 G. Rein, "Selfgravitating systems in Newtonian theory—the Vlasov-Poisson system, Mathematics of gravitation, Part I" Banach Center Publ. 179-194, 1997

      15 P.-L. Lions, "Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system" 105 (105): 415-430, 1991

      16 C. Bardos, "Probl`emes aux limites pour les ´equations aux d´erivees partielles du premier ordre `a coefficients r´eels; th´eorem`es d’approximation; application `a l’´equation de transport" 4 (4): 185-233, 1970

      17 R. J. Diperna, "Ordinary differential equations, transport theory and Sobolev spaces" 98 (98): 511-547, 1989

      18 R. Glassey, "On the “one and one-half dimensional” relativistic Vlasov-Maxwell system" 13 (13): 169-179, 1990

      19 S. Mischler, "On the trace problem for solutions of the Vlasov equation" 25 (25): 1415-1443, 2000

      20 S. Calogero, "On classical solutions of the Nordstr¨om-Vlasov system" 28 (28): 1863-1885, 2003

      21 G. Rein, "Non-linear stability for the Vlasov-Poisson system-the energy-Casimir method" 17 (17): 1129-1140, 1994

      22 P. Degond, "Local existence of solutions of the Vlasov-Maxwell equations and convergence to the Vlasov-Poisson equations for infinite light velocity" 8 (8): 533-558, 1986

      23 J. Batt, "Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions" 130 (130): 163-182, 1995

      24 S. Calogero, "Global weak solutions to the Nordstr¨om-Vlasov system" 204 (204): 323-338, 2004

      25 Y. Guo, "Global weak solutions of the Vlasov-Maxwell system with boundary conditions" 154 (154): 245-263, 1993

      26 R. J. Diperna, "Global weak solutions of Vlasov-Maxwell systems" 42 (42): 729-757, 1989

      27 J. Schaeffer, "Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions" 16 (16): 1313-1335, 1991

      28 G. Rein, "Global existence of classical solutions to the Vlasov-Poisson system in a three-dimensional, cosmological setting" 126 (126): 183-201, 1994

      29 A. Arsen’ev, "Global existence of a weak solution of the Vlasov system of equations" 15 : 131-143, 1975

      30 K. Pfaffelmoser, "Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data" 95 (95): 281-303, 1992

      31 G. Rein, "Existence of stationary, collisionless plasmas in bounded domains" 15 (15): 365-374, 1992

      32 F. Bouchut, "Classical solutions and the Glassey-Strauss theorem for the 3D Vlasov-Maxwell system" 170 (170): 1-15, 2003

      33 F. Poupaud, "Boundary value problems for the stationary Vlasov-Maxwell system" 4 (4): 499-527, 1992

      34 M. Bostan, "Boundary value problem for the three dimensional time periodic Vlasov-Maxwell system" 3 (3): 621-663, 2005

      35 J. Dolbeault, "Asymptotic behaviour for the Vlasov-Poisson system in the stellar-dynamics case" 171 (171): 301-327, 2004

      36 M. Bostan, "Asymptotic behavior of weak solutions for the relativistic Vlasov-Maxwell equations with large light speed" 227 (227): 444-498, 2006

      37 A. D. Rendall, "An introduction to the Einstein-Vlasov system, Mathematics of gravitation, Part I" Banach Center Publ. 35-68, 1997

      38 S. Klainerman, "A new approach to study the Vlasov-Maxwell system" 1 (1): 103-125, 2002

      39 C. Greengard, "A boundary-value problem for the stationary Vlasov-Poisson equations: the plane diode" 43 (43): 473-507, 1990

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