Stationary voltage current characteristics of a plasma
Ben Abdallah, Naoufel ; Unterreiter, Andreas
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 30 (1996), p. 575-605 / Harvested from Numdam
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Publié le : 1996-01-01
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     author = {Ben Abdallah, Naoufel and Unterreiter, Andreas},
     title = {Stationary voltage current characteristics of a plasma},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {30},
     year = {1996},
     pages = {575-605},
     mrnumber = {1411392},
     zbl = {0865.76100},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1996__30_5_575_0}
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Ben Abdallah, Naoufel; Unterreiter, Andreas. Stationary voltage current characteristics of a plasma. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 30 (1996) pp. 575-605. http://gdmltest.u-ga.fr/item/M2AN_1996__30_5_575_0/

[1] C. Bardos and P. Degond, 1985, Global Existence for the Vlasov-Poisson Equation in 3 Space with Small Initial Data, Ann. Inst. Henri Poincaré, Analyse non linéaire, 2(2), pp.101-118. | Numdam | MR 794002 | Zbl 0593.35076

[2] J. Batt, H. Berestycki, R. Degond and B. Perthame, 1988, Some Families of Solutions of the Vlasov-Poisson System, Arch. Rat. Mech. Anal, 104(1), pp. 79-103. | MR 956568 | Zbl 0703.35171

[3] N. Benabdallah, 1994, The Child-Langmuir Regime for Electron Transport in a Plasma Including a Background Density of Positive Ions, M3 AS, 4(3), pp, 409-438. | MR 1282242

[4] N. Benabdallah, 1994, Étude de modèles asymptotiques de transport de particules chargées : Asymptotique de Child-Langmuir, PhD thesis, Centre de Mathématiques Appliquées, École Polytechnique, F-91128 Palaiseau Cedex.

[5] N. Benabdallah, P. Degond and C. Schmeiser, 1994, On a Mathematical Model for Hot Carrier Injection in Semiconductors, M2 AS, 17, pp.1193-1212. | MR 1313133 | Zbl 0812.35137

[6] P. Degond and P. A. Raviart, 1991, An Asymptotic Analysis of the One Dimensional Vlasov-Poisson System : the Child-Langmuir Law, Asymptotic Analysis, 4, pp.187-214. | MR 1115929 | Zbl 0840.35082

[7] P. Degond, S. Jaffard, F. Poupaud, P. A. Raviart. The Child-Langmuir Asymptotics of the Vlasov-Poisson Equation for Cylindrically or Spherically Symmetrie Diodes, Part 1 : Statement of the Problem and Basic Estimates. Technical Report 264, CMAP, École Polytechnique, F-91128 Palaiseau Cedex, 1992. | Zbl 0844.35086

[8] R. T. Glassey and J. W. Schaeffer, 1985, On Symmetrie Solutions of the Relativistic Vlasov-Poisson System, Comm. Math. Phys., 101, pp. 459-473. | MR 815195 | Zbl 0582.35110

[9] R. T. Glassey and J. W. Schaeffer, 1988, Global Existence for the Relativistic Vlasov-Maxwell System with Nearly Neutral Initial Data, Comm. Math. Phys., 119, pp. 353-384. | MR 969207 | Zbl 0673.35070

[10] R. T. Glassey and W. A. Strauss, Singularity Formation in a Collisionless Plasma Could Occur Only at High Velocities, Arch. Rat. Mech. Anal, 92(1), pp. 59-90. | MR 816621 | Zbl 0595.35072

[11] R.T. Glassey and W.A. Strauss, 1987, Absence of Shocks in an Initially Dilute Collisionless Plasma, Comm. Math. Phys., 113, pp. 191-208. | MR 919231 | Zbl 0646.35072

[12] C. Greengard and P. A. Raviart, 1990, A Boundary Value Probiem for the Stationary Vlasov-Poisson Equations : the Plane Diode, Comm. Pure. Appl. Math., 43, pp. 473-507. | MR 1047333 | Zbl 0721.35084

[13] St. Humphries, 1990, Charged Particle Beams, John Wiley & Sons.

[14] L. D. Landau and E. M. Llfschitz, 1987, Lehrbuch der theoretischen Physik. Teil 2. Klassische Feldtheorie, Akademie Verlag, Berlin, l0th edition. | MR 893181

[15] M. Marcus and V. J. Mizel, 1972, Absolute Continuity on Tracks and Mappings of Sobolev Spaces, Arch. Rat. Mech. Anal., pp. 294-320. | MR 338765 | Zbl 0236.46033

[16] R.J. Di Perna and P. L. Lions, 1989, Global Weak Solutions of Vlasov-Maxwell Systems, Comm. Pure Appl. Math., 42, pp. 729-757. | MR 1003433 | Zbl 0698.35128

[17] F. Poupaud, 1992, Boundary Value Problems for the Stationary Vlasov-Maxwell systems, Forum Mathematicum, 4, pp. 499-527. | MR 1176884 | Zbl 0785.35020

[18] W. P. Zlemer, 1989, Weakly Differentiable Functions, Springer. | MR 1014685 | Zbl 0692.46022