Système Euler-Poisson non linéaire. Existence globale de solutions faibles entropiques

Stéphane Cordier; Yue-Jun Peng

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1998)

  • Volume: 32, Issue: 1, page 1-23
  • ISSN: 0764-583X

How to cite

top

Cordier, Stéphane, and Peng, Yue-Jun. "Système Euler-Poisson non linéaire. Existence globale de solutions faibles entropiques." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 32.1 (1998): 1-23. <http://eudml.org/doc/193865>.

@article{Cordier1998,
author = {Cordier, Stéphane, Peng, Yue-Jun},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {equations for ions coupled with the Poisson equation involving Maxwellian electrons; Glimm scheme},
language = {fre},
number = {1},
pages = {1-23},
publisher = {Dunod},
title = {Système Euler-Poisson non linéaire. Existence globale de solutions faibles entropiques},
url = {http://eudml.org/doc/193865},
volume = {32},
year = {1998},
}

TY - JOUR
AU - Cordier, Stéphane
AU - Peng, Yue-Jun
TI - Système Euler-Poisson non linéaire. Existence globale de solutions faibles entropiques
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1998
PB - Dunod
VL - 32
IS - 1
SP - 1
EP - 23
LA - fre
KW - equations for ions coupled with the Poisson equation involving Maxwellian electrons; Glimm scheme
UR - http://eudml.org/doc/193865
ER -

References

top
  1. [1] N. BEN ABDALLAH, S. MAS-GALLIC, P.-A. RAVIART, 1995, Analysis and asymptotics of a one dimensional ion extraction model, Asymp. Analysis, Vol. 10, p. 1-28. Zbl0829.76096MR1319009
  2. [2] B. BODIN, 1995, Thèse de l'école Polytechnique, CMAP. 
  3. [3] F. CHEN, 1974, « Introduction to Plasmas Physics », Plenum Press, New York, 1974. 
  4. [4] S. CORDIER, 1995, Global solutions to the isothermal Euler-Poisson system with arbitrary large data for a plasma, Appl. Math. Lett., Vol. 8, n° 1, p 19-24. Zbl0817.76102MR1355145
  5. [5] S. CORDIER, P. DEGOND, P. MARKOWICH, C. SCHMEISER, 1995, Travelling Wave analysis for Isothermal Euler-Poisson Model of a Plasma, Annales de la Faculté des Sciences de Toulouse, Vol. V, N° 4, p 599-645. Zbl0884.35126MR1473076
  6. [6] S. CORDIER, E. GRENIER, 1996, Quasineutral limit of Euler-Poisson systems, prépublication du Laboratoire d'analyse numérique, université Paris 6, N° 96030. 
  7. [7] J. L. DELCROIX, A. BEERS, 1994, Physique des Plasmas, CNRS Editions. 
  8. [8] S. FABRE, 1995, Étude de l'équation de Poisson couplée à la relation de Boltzmann dans RN et quasi neutralité. Note aux comptes rendus de l'académie des sciences, t. 320, Série I, p. 45-48. Zbl0831.76099MR1320829
  9. [9] J. GLIMM, 1965, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure. Appl. Math., 18 : 698-715. Zbl0141.28902MR194770
  10. [10] F. GLOSE, R. SENTIS, 1993, Analyse asymptotique de l'équation de Poisson couplée à la relation de Boltzmann. Quasineutralité des plasmas, rapport CEA. 
  11. [11] E. GRENIER, 1994, Oscillations in quasineutral plasmas, Comm. PDE, Vol. 31, p 361-394, 1996. Zbl0849.35107MR1387452
  12. [12] P. LE FLOCH, 1990, The random choice method applied to the quasilinear hyperbolic systems, R.I. CMAP 218, École polytechnique. 
  13. [13] P. H. MAIRE, 1994, Ionisation dans un écoulement aérodynamique, Note C.E.A. 2774. 
  14. [14] P. MARCATI, R. NATALINI, 1995, Weak solutions to a hydrodynamic model for semiconductors : the Cauchy problem, Proc. Roy. Soc. Edimburg, Sect. A, 125, p. 115-131. Zbl0831.35157MR1318626
  15. [15] P. A. MARKOWICH, C. A. RINGHOFFER, C. SCHMEISER, 1986, An asymptotic analysis of one dimensional semiconductor devices, IMA, J. Applied Math., 37, pp. 1-24. Zbl0639.34016MR983515
  16. [16] S. MAS-GALLIC, P. A. RAVIART, 1994, Mathematical models of ion extraction and plasma sheaths, G.d.R. S.PAR.CH. 11, Ecole Polytechnique, Palaiseau, France. Zbl0863.76095MR1323181
  17. [17] T. NISHIDA, 1968, Global solutions for an initial boundary value problem of a quasilinear hyperbolic system, Japan. Acad., 44 : 642-646, 1968. Zbl0167.10301MR236526
  18. [18] F. POUPAUD, M. RASCLE, J. P. VILA, 1994, Global solutions to the isothermal Euler-Poisson system with arbitrary large data, Jal of Diff. Eq. 1995, p. 93-121, Vol. 123. Zbl0845.35123MR1359913
  19. [19] C. SCHMEISER, 1993, Personnal communication. 
  20. [20] SMOLLER, 1987, Shock waves and reaction diffusion equations, Grundlehren in Mathematisschen Wissenschaft, Springer Verlag, no 258. Zbl0807.35002

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.