A hierarchy of hydrodynamic models for plasmas zero-relaxation-time limits

References

• Adams , R.A. 1981 . Sobolev Space , Academic Press .
   Google Scholar
• G.Q. Chen, The theory of compensated compactness and the system of isentropic gas dynamics, preprint. MCS-P154-0590. 1990. Univ. of Chicago.
   Google Scholar
• Chen , G. Q. , Levermore , C. D. and Liu , T. P. 1994 . Hyperbolic conservation laws with stiff relaxation terms and entropy . Comm. Pure Appl. Math. , 47 : 787 – 830 .
   Web of Science ®Google Scholar
• Cordier , S. 1994 . Global solutions to the isothermal Euler-Poisson plasma model . Appl. Math. Lett. , 8 : 19 – 24 .
   Web of Science ®Google Scholar
• S. Cordier and E. Grenier, Quasineutral limit of Euler-Poisson system. preprint. 1996, LAN, Univ. Paris 6.
   Google Scholar
• Cordier , S. and Peng , Y. J. 1998 . Systkme Euler-Poisson non linkaire - Existence globale de solutions faibles entropiques . Mod. Math. Anal. Num. , 32 ( 1 ) : 1 – 23 .
   Web of Science ®Google Scholar
• DiPerna , R. J. 1983 . Convergence of the viscosity method for isentropic gas dynamics . Comm. Math. Phys. , 91 ( 1 ) : 1 – 30 .
   Web of Science ®Google Scholar
• Gardner , C. 1991 . Numerical simulation of a steady-state electron shock wave in a submicron semiconductor device . IEEE Trans. El. Dev. , 38 : 392 – 398 .
   Web of Science ®Google Scholar
• Th. Goudon, A. Jiingel and Y.J. Peng, Zero-electron-mass limits in hydrodynamic models for plasmas, Appl. Math. Letters, to appear.
   Google Scholar
• Jiang , X. 1995 . A streamline-upwinding/Petrov-Galerkin method for the hydrodynamic semiconductor device model. . Math. Models Meth. Xppl. Sci. , 5 : 659 – 681 .
   Web of Science ®Google Scholar
• Jin , S. and Xin , Z. 1995 . The relaxation schemes for systems of conservation laws in arbitrary space dimensions. . Comm. Pure Appl. Math. , 48 : 235 – 277 .
   Web of Science ®Google Scholar
• S. Junca and M. Rascle, Relaxation of the isothermal Euler-Poisson s>5- tem to the drift-diffusion equations. Quart. Appl. Math. to appear.
   Google Scholar
• Jungel , A. 1994 . On the existence and uniqueness of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors. . Math. Slod. 1Ieth. Appl. Sci. , 4 ( 5 ) : 677 – 703 .
   Web of Science ®Google Scholar
• Jungel , A. 1997 . A nonlinear drift-diffusion system with electric convection arising in electrophoretic and semiconductor modeling. . Math. Nachr. , 185 : 85 – 110 .
   Web of Science ®Google Scholar
• A. Jdngel and Y.J. Peng. A hierarchy of hydrodynamics models for plasmas : Zero-mass-electron limits. preprint. No. 98-1. 1998. LSlA. Univ. Blaise Pascal.
   Google Scholar
• Lions , P. L. , Perthame , B. and Souganidis , P. E. 1996 . Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates . Comm. Pure Appl. Math. , 49 : 599 – 638 .
   Web of Science ®Google Scholar
• Lions , P. L. , Perthame , B. and Tadmor , E. 1994 . Kinetic formulation for the isentropic gas dynamics and p-system . Comrn. Math. Phys. , 163 : 415 – 431 .
   Web of Science ®Google Scholar
• Liu , T. P. 1987 . Hyperbolic conservation laws with relaxation. . Comm. Math. Phys. , 108 : 153 – 175 .
   Web of Science ®Google Scholar
• Marcati , P. and Natalini , R. 1995 . Weak solutions to a hydrodynamic model for semiconductors:the Cauchy problem . Proc. Roy. Soc. Edinburgh Sect. A , 125 : 115 – 131 .
   Google Scholar
• Marcati , P. and Natalini , R. 1995 . Weak solutions to a hydrodynamic model for semiconductors and Relaxation to the drift-diffusion equation. . Arch. Rat. Mech. Anal. , 129 : 129 – 145 .
   Web of Science ®Google Scholar
• Murat , F. 1978 . Cornpacite par compensation . Ann. Sc. Norm. Sup. Pisa. , 5 : 489 – 507 .
   Google Scholar
• Natalini , R. 1996 . The bipolar hydrodynamic model for semiconductors and the drift-diffusion equation . J. Math. Analysis and Appl. , 198 : 262 – 281 .
   Web of Science ®Google Scholar
• Natalini , R. 1996 . Convergence to equilibrium for the relaxation approximations of conservation laws . Comm. Pure Appl. Math. , 49 : 795 – 823 .
   Web of Science ®Google Scholar
• Y.J. Peng, Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for a nonlinear Euler-Poisson system. Nonlinear Analysis TMA, to appear.
   Google Scholar
• Poupaud , F. , Rasle , M. and Global , J. P. 1995 . Global solutions to the isothermal Euler-Poisson system with arbitrary large data. . J. Diff. Eqn. , 123 : 93 – 121 .
   Web of Science ®Google Scholar
• Raviart , P. A. 1997 . On singular perturbation problems for the nonlinear Poisson equation or . A mathematical approach to electrostatic sheaths and plasma erosion. Lecture Notes of the Summer school in Ile d'014ron. France. , : 452 – 539 .
   Google Scholar
• D. Serre, Relaxation semi-linkaire et cinktique des systkmes de lois de conservation, preprint, ENS-Lyon, No.228, 1998.
   Google Scholar
• Tartar , L. 1979 . Compensated compactness and applications to partial differential equations, Research Note in mathematics Edited by: Knops , R. J. 136 – 212 . nonlinear analysis andmechanics, Heriot-Watt symposium, .
   Google Scholar
• 1982 . Singular perturbations of first order hyperbolic systems , Universitat Heidelberg .
   Google Scholar