Problème aux limites pour le système de Vlasov-Maxwell
Séminaire Équations aux dérivées partielles (Polytechnique) (1992-1993), Talk no. 4, 17 p.
@article{SEDP_1992-1993____A4_0,
     author = {Bezard, M.},
     title = {Probl\`eme aux limites pour le syst\`eme de Vlasov-Maxwell},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
     publisher = {Ecole Polytechnique, Centre de Math\'ematiques},
     year = {1992-1993},
     note = {talk:4},
     zbl = {0878.35107},
     mrnumber = {1240545},
     language = {fr},
     url = {http://www.numdam.org/item/SEDP_1992-1993____A4_0}
}
Bezard, M. Problème aux limites pour le système de Vlasov-Maxwell. Séminaire Équations aux dérivées partielles (Polytechnique) (1992-1993), Talk no. 4, 17 p. http://www.numdam.org/item/SEDP_1992-1993____A4_0/

[1] Agmon, Douglas, Nirenberg, Estimates near the boundary of solutions of elliptic partial differential equations satisfying general boundary conditions, I. CPAM 12 (1959), pp. 623-726, II. CPAM 17 (1964), pp 35-92. | MR 162050 | Zbl 0123.28706

[2] Alinhac, Existence d'ondes de raréfaction pour de systèmes quasilinéaires hyperboliques multidimensionnels, CPDE 14 (1989), pp 173-230. | MR 976971 | Zbl 0692.35063

[3] Asano, On local solutions of the initial valve problem for the Vlasov-Maxwell system, CMP 106 (1986), pp 551-568. | MR 860309 | Zbl 0631.76090

[4] Bardos-Degond, Global existence for the Vlasov-Poisson equation in 3-space variable with small initial data, Ann. Inst. H. Poincaré, Anal. Inst. H. Poincaré, Anal. Nonlinéaire 2 (1985), pp. 101-118. | Numdam | MR 794002 | Zbl 0593.35076

[5] Batt, Global symmetric solutions of the initial value problem of stellar dynamic, J. diff. eq. 25 (1977), pp. 342-364. | MR 487082 | Zbl 0366.35020

[6] Bezard, Problème de Riemann généralisé pour un système de lois de conservation multidimensionnel vraiment non linéaire. Proceedings "Journées EDP St. Jean de Monts" Ed. Ecole Polytechnique, France + manuscrit. | Numdam | MR 1069967 | Zbl 0704.35092

[7] Cessenat, Théorèmes de trace LP pour les espaces de fonction de la neutronique, C.R. Ac. Sci., Paris 299 (1986), pp. 831-834, et C.R. Ac. Sci. Paris 300 (1985), pp. 89-92. | MR 777741 | Zbl 0648.46028

[8] Chazarain-Piriou, Introduction à la théorie des équations aux dérivées partielles linéaires. Gauthier Villars 1981. | MR 598467 | Zbl 0446.35001

[9] Dautray-Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, 3 vol. Masson, 1983. | Zbl 0642.35001

[10] Degond, Régularité des solutions des équations cinétiques en physique des plasmas. Séminaire EDP 1985-1986, Ecole Polytechnique, France. | Numdam | Zbl 0613.35070

[11] Degond-Raviart, An analysis of the Darwin model of approximation to Maxwell's equation, Preprint CMAP, Ecole Polytechnique, n°213, Mars 1990. | Zbl 0755.35137

[12] Di Perna-Lions, On Fokker-Planck-Boltzmann equation, CMP 120 (1988), pp. 1-23. | MR 972541 | Zbl 0671.35068

[13] Di Perna-Lions, On the Cauchy problem for Boltzmann equation: global existence and weak stability, Ann. Math. 130 (1989), pp. 321-366. | MR 1014927 | Zbl 0698.45010

[14] Di Perna-Lions, Solutions globales pour les équations de Vlasov-Poisson, C.R. Acad. Sci. 307 (1988), pp. 655-658. | MR 967806 | Zbl 0682.35022

[15] Di Perna-Lions, Global weak solutions of Vlasov-Maxwell systems, CPAM 42 (1989), pp 729-757. | MR 1003433 | Zbl 0698.35128

[16]Friederichs, Well-posed problems of mathematical physics, Mimeographed Lecture Notes, NYU.

[17]Friederichs, Symmetric positive systems of differential equations, CPAM 11 (1959), pp. 333-418. | Zbl 0083.31802

[18]Gårding, Le problème de la dérivée oblique pour l'équation des ondes, C.R. Acad. Sci. Paris, 285 (1977), pp. 773-775, + Rectifications CRAS 285 (1977), p.1199. | Zbl 0386.35024

[19] Glassey-Strauss, Singularity formation in a collisionless plasma could occur only at high velocities, Arch. Rat. Mech. Anal, 92 (1986), pp. 59-90. | MR 816621 | Zbl 0595.35072

[20] Greengard-Raviart, A boundary value problem for the stationary Vlasov-Poisson equations: the plane diode, CPAM 43 (1990), pp. 473-507. | MR 1047333 | Zbl 0721.35084

[21] Gués, Problème mixte hyperbolique quasi-linéaire caractéristique, CPDE 15 (1990), pp. 595-646. | MR 1070840 | Zbl 0712.35061

[22] Hamdache, Problème aux limites pour l'équation de Boltzmann, existence globale de solutions, CPDE 13 (1988), pp. 813-845. | MR 940959 | Zbl 0668.76090

[23] Haus-Melcher, Electromagnetic fields and energy, Englewood Cliffs, Prentice Hall.

[24] Hörmander, The analysis of linear partial differential operators, 4 vol. Springer.

[25] Jackson, Classical electrodynamics, Wiley. | Zbl 0114.42903

[26] Kato, Perturbation theory for linear operators, Springer. | Zbl 0148.12601

[27]Kreiss, Initial boundary value problems for hyperbolic systems, CPAM, 23 (1970), pp. 277-298. | MR 437941 | Zbl 0193.06902

[28] Lawson, The physics of charged particle beams, Oxford Clarendon Press.

[29] J-L. Lions, Perturbation singulières dans les problèmes aux limites, et contrôle optimal, LNM 323, Springer. | Zbl 0268.49001

[30] P-L. Lions, Kinetic equations, Lecture ICM, Kyoto 90. | Zbl 0806.35143

[31] Majda-Osher, Initial boundary value problems for hyperbolic equations with uniformly characteristic boundary, CPAM, 28 (1975), pp. 607-695. | MR 410107 | Zbl 0314.35061

[32] Nishida-Rauch, Local existence for smooth inviscid compressible flows in bounded domains, Manuscript (1985).

[33] Panofsky-Phillips, Classical electricity and magnetism, Addison Wesley. | Zbl 0122.21401

[34] Poupaud, Solutions stationnaires des équations de Vlasov-Poisson, C.R. Ac. Sci. Paris 311 (1990), pp. 307-312. | MR 1071632 | Zbl 0711.35139

[35] Poupaud, Boundary value problems for the stationary Vlasov-Maxwell systems, Preprint Nice 1991. | Zbl 0785.35020

[36] Rauch, Symmetric positive systems with boundary characteristics of constant multiplicity, Trans. AMS, 291, (1985), pp. 167-187. | MR 797053 | Zbl 0549.35099

[37] Raviart, Approximate models for Maxwell's system and applications, Preprint, CMAP, Ecole Polytechnique, No 227.

[38] Rendal-Rein, On Vlasov-Einstein, Preprint.

[39] Sakamoto, Mixed problems for hyperbolic equations, I-II Math. J. Kyoto Univ. pp. 349-373; 403-417, vol 10 (1970). | Zbl 0203.10001

[40] Schochet, The compressible Euler equations in a bounded domain: existence of solution and incompressible limit, CMP 106 (1986), pp. 69-75. | Zbl 0612.76082

[41] Strauss, Nonlinear wave equations, CBMS, Regional conference in Math No 73, AMS 1990. | Zbl 0714.35003

[42] Ukai, Solutions of the Boltzmann system in "Pattern and waves" Ed. Nishida-Mimura-Fuji, North Holland.

[43] Ukai-Asano, On the Vlasov-Poisson limit of the Vlasov-Maxwell equations, in " Pattern and waves" Ed. Nishida-Mimura-Fuji, North Holland. | Zbl 0623.35059

[44] Ukai-Asano, Steady solutions of the Boltzmann equation for a gas flow past an obstacle, Archiv. Rat. Mech. Anal. 84 (1983), pp. 269-291. | Zbl 0538.76070

[45] Wollmann, An existence and uniqueness theorem for the Vlasov-Maxwell system, CPAM 37 (1986), pp. 651-662. | Zbl 0592.45010

[46] Yosida, Functional analysis, Springer.

[47] Beals-Protopopescu, Abstract time-dependant transport equations, J. Math. Anal. Appl. (1987), pp. 370-405. | MR 872231 | Zbl 0657.45007

[48] Bezard, Problème aux limites pour le système de Vlasov-Maxwell Preprint 1991, Soumis Archiv Rat. Mech. Anal.

[49] Bezard, Existence globale pour le système de Vlasov-Darwin. En préparation

[50] Guo, Global weak solutions of the Vlasov-Maxwell system. Preprint Brown University 1991.