Global Existence and Relaxation Limit for Smooth Solutions to the Euler--Poisson Model for Semiconductors, SIAM Journal on Mathematical Analysis, vol.32, issue.3, pp.572-587, 2000. ,
DOI : 10.1137/S0036141099355174
The zero-electron-mass limit in the hydrodynamic model for plasmas, pp.72-4415, 2010. ,
Global smooth solutions to the multi-dimensional hydrodynamic model for two-carrier plasmas, Journal of Differential Equations, vol.190, issue.2, pp.663-685, 2003. ,
DOI : 10.1016/S0022-0396(02)00157-2
Subsonic solutions to a onedimensional non-isentropic hydrodynamic model for semiconductors, J. Math. Anal. Appl, pp.258-53, 2001. ,
Analysis and asymptotics of a one dimensional ion extraction model, Asymp, Analysis, vol.10, pp.1-28, 1995. ,
A MODEL HIERARCHY FOR IONOSPHERIC PLASMA MODELING, Mathematical Models and Methods in Applied Sciences, vol.14, issue.03, pp.393-415, 2004. ,
DOI : 10.1142/S0218202504003283
URL : https://hal.archives-ouvertes.fr/hal-00018457
Asymptotic behavior of weak solutions for the relativistic Vlasov???Maxwell equations with large light speed, Journal of Differential Equations, vol.227, issue.2, pp.444-498, 2006. ,
DOI : 10.1016/j.jde.2005.10.018
Incompressible Euler and E-MHD as scaling limits of the Vlasov-Maxwell system, Communications in Mathematical Sciences, vol.1, issue.3, pp.437-447, 2003. ,
DOI : 10.4310/CMS.2003.v1.n3.a4
Introduction to Plasma Physics and Controlled Fusion, 1984. ,
Basic aspects of hyperbolic relaxation systems, in Advances in the Theory of Shock Waves, H. Freistühler and A. Szepessy, Progr, Nonlinear Differential Equations Appl, vol.47, pp.259-305, 2001. ,
Compressible Euler-Maxwell equations, Transport Theory and Statistical Physics, vol.4, issue.3-5, pp.29-311, 2000. ,
DOI : 10.1007/978-3-7091-6961-2
Global solutions to the isothermal Euler-Poisson plasma model, Applied Mathematics Letters, vol.8, issue.1, pp.19-24, 1995. ,
DOI : 10.1016/0893-9659(94)00104-K
Travelling Wave analysis for Isothermal Euler-Poisson Model of a Plasma, pp.4-599, 1995. ,
Quasineutral limit of an Euler-Poisson system arising from plasma physics Commun, Partial Diff, Eqns, pp.25-1099, 2000. ,
A steady state potentiel flow model for semi-conductors, IV), pp.87-98, 1993. ,
On a one-dimensional steady-state hydrodynamic model for semiconductors, Applied Mathematics Letters, vol.3, issue.3, pp.25-29, 1990. ,
DOI : 10.1016/0893-9659(90)90130-4
Symmetric hyperbolic linear differential equations, Communications on Pure and Applied Mathematics, vol.88, issue.2, pp.345-392, 1954. ,
DOI : 10.1002/cpa.3160070206
Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductors, Comm. Part. Diff. Eqs, vol.17, pp.553-577, 1992. ,
A viscous approximation for a 2-D steady semiconductor or transonic gaz dynamic flow : existence theorem for potential flow, Comm. Pure Appl. Math. XLIX, pp.999-1049, 1996. ,
The energy transport and the drift diffusion equations as relaxation limits of the hydrodynamic model for semiconductors, Quarterly of Applied Mathematics, vol.57, issue.2, pp.269-282, 1999. ,
DOI : 10.1090/qam/1686190
Numerical methods for nonlinear variational problems, 1984. ,
Analyse asymptotique de l'équation de Poisson couplée Ã? la relation de Boltzmann, 1993. ,
Oscillations in quasineutral plasmas, Communications in Partial Differential Equations, vol.26, issue.2, pp.31-361, 1996. ,
DOI : 10.1080/03605309608821189
Stability of Semiconductor States with Insulating and Contact Boundary Conditions, Archive for Rational Mechanics and Analysis, vol.242, issue.1, pp.1-30, 2006. ,
DOI : 10.1007/s00205-005-0369-2
Initial layers and zero-relaxation limits of Euler???Maxwell equations, Journal of Differential Equations, vol.252, issue.2, pp.1441-1465, 2012. ,
DOI : 10.1016/j.jde.2011.09.029
Initial layers and zero-relaxation limits of multidimensional Euler-Poisson equations, Mathematical Methods in the Applied Sciences, vol.53, issue.2, 2011. ,
DOI : 10.1002/mma.2580
Global Existence of Smooth Solutions for Partially Dissipative Hyperbolic Systems with a Convex Entropy, Archive for Rational Mechanics and Analysis, vol.169, issue.2, pp.89-117, 2003. ,
DOI : 10.1007/s00205-003-0257-6
The asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors, Journal of Differential Equations, vol.192, issue.1, pp.111-133, 2003. ,
DOI : 10.1016/S0022-0396(03)00063-9
Asymptotics of Initial Boundary Value Problems for Hydrodynamic and Drift Diffusion Models for Semiconductors, Journal of Differential Equations, vol.170, issue.2, pp.472-493, 2001. ,
DOI : 10.1006/jdeq.2000.3825
THE GLOBAL WEAK SOLUTION AND RELAXATION LIMITS OF THE INITIAL???BOUNDARY VALUE PROBLEM TO THE BIPOLAR HYDRODYNAMIC MODEL FOR SEMICONDUCTORS, Mathematical Models and Methods in Applied Sciences, vol.10, issue.09, pp.1333-1361, 2000. ,
DOI : 10.1142/S0218202500000653
The Relaxation of the Hydrodynamic Model for Semiconductors to the Drift???Diffusion Equations, Journal of Differential Equations, vol.165, issue.2, pp.315-354, 2000. ,
DOI : 10.1006/jdeq.2000.3780
Introduction à l'analyse mathématiques des équations de Maxwell en régime transitoire, 1994. ,
Relaxation of the isothermal Euler-Poisson system to the drift-diffusion equations, Quarterly of Applied Mathematics, vol.58, issue.3, pp.511-521, 2000. ,
DOI : 10.1090/qam/1770652
URL : https://hal.archives-ouvertes.fr/hal-01312342
A hierarchy of hydrodynamic models for plasmas zero-relaxation-time limits, Communications in Partial Differential Equations, vol.5, issue.5-6, pp.1007-1033, 1999. ,
DOI : 10.1006/jdeq.1995.1158
Zero-relaxation-time limits in the hydrodynamic equations for plasmas revisited, Zeitschrift f??r angewandte Mathematik und Physik, vol.51, issue.3, pp.385-396, 2000. ,
DOI : 10.1007/s000330050004
The Cauchy problem for quasi-linear symmetric hyperbolic systems, Archive for Rational Mechanics and Analysis, vol.168, issue.3, pp.181-205, 1975. ,
DOI : 10.1007/BF00280740
Smooth global solutions for two-dimensional equations of electro-magneto-fluid dynamics, Japan Journal of Applied Mathematics, vol.16, issue.3, pp.207-222, 1984. ,
DOI : 10.1007/BF03167869
Systems of a hyperbolic-parabolic composite type, with applications to the equations of magneto-hydrodynamics, Doctoral Thesis, pp.245-364, 1984. ,
Dissipative Structure and Entropy for Hyperbolic Systems of Balance Laws, Archive for Rational Mechanics and Analysis, vol.172, issue.3, pp.345-364, 2004. ,
DOI : 10.1007/s00205-004-0330-9
Compressible and incompressible fluids, Communications on Pure and Applied Mathematics, vol.33, issue.5, pp.629-651, 1982. ,
DOI : 10.1002/cpa.3160350503
Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Communications on Pure and Applied Mathematics, vol.71, issue.4, pp.481-524, 1981. ,
DOI : 10.1002/cpa.3160340405
ON THE 3-D BIPOLAR ISENTROPIC EULER???POISSON MODEL FOR SEMICONDUCTORS AND THE DRIFT-DIFFUSION LIMIT, Mathematical Models and Methods in Applied Sciences, vol.10, issue.03, pp.351-360, 2000. ,
DOI : 10.1142/S0218202500000215
The relaxation to the drift-diffusion system for the 3-D isentropic Euler-Poisson model for semiconductors, Discrete Contin, Dynam. Systems, vol.5, pp.449-455, 1999. ,
HYPERBOLIC-PARABOLIC SINGULAR LIMITS FOR FIRST-ORDER NONLINEAR SYSTEMS, Communications in Partial Differential Equations, vol.155, issue.5-6, pp.939-964, 2001. ,
DOI : 10.1137/S0036139999352705
Asymptotic behaviour of solutions of the hydrodynamic model of semiconductors, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.132, issue.02, pp.359-378, 2002. ,
DOI : 10.1017/S0308210500001670
large time behavior of the solutions to a hydrodynamic model for semiconductors, SIAM J. Appl. Math, pp.95-810, 1998. ,
Ionisation dans un écoulement aérodynamique, Note C, E.A, p.2774, 1994. ,
Compressible Fluid flow and Systems of Conservation Laws in Several Space Variables, 1984. ,
DOI : 10.1007/978-1-4612-1116-7
Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation, Archive for Rational Mechanics and Analysis, vol.157, issue.2, pp.129-145, 1995. ,
DOI : 10.1007/BF00379918
Hyperbolic to Parabolic Relaxation Theory for Quasilinear First Order Systems, Journal of Differential Equations, vol.162, issue.2, pp.359-399, 2000. ,
DOI : 10.1006/jdeq.1999.3676
An Asymptotic Analysis of One-Dimensional Models of Semiconductor Devices, IMA Journal of Applied Mathematics, vol.37, issue.1, pp.1-24, 1986. ,
DOI : 10.1093/imamat/37.1.1
MATHEMATICAL MODELS OF ION EXTRACTION AND PLASMA SHEATHS, G.G.R. S.PAR.CH. École Polytechnique, vol.11, 1994. ,
DOI : 10.1142/9789814354165_0003
The Bipolar Hydrodynamic Model for Semiconductors and the Drift???Diffusion Equations, Journal of Mathematical Analysis and Applications, vol.198, issue.1, pp.262-281, 1996. ,
DOI : 10.1006/jmaa.1996.0081
Relaxation limit and initial layer to hydrodynamic models for semiconductors, Journal of Differential Equations, vol.249, issue.6, pp.1385-1409, 2010. ,
DOI : 10.1016/j.jde.2010.06.008
Some asymptotic analysis in steady state Euler-Poisson equations for potential flow, Asymptotic analysis, pp.75-92, 2003. ,
Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters, Discrete Contin, Dynnam. Syst, vol.23, pp.415-433, 2009. ,
Convergence of Compressible Euler-Maxwell Equations to Compressible Euler-Poisson Equations*, Chinese Annals of Mathematics, Series B, vol.31, issue.5, pp.583-602, 2007. ,
DOI : 10.1007/s11401-005-0556-3
URL : https://hal.archives-ouvertes.fr/hal-00489068
Convergence of Compressible Euler???Maxwell Equations to Incompressible Euler Equations, Communications in Partial Differential Equations, vol.41, issue.3, pp.33-349, 2008. ,
DOI : 10.1080/03605300500361487
URL : https://hal.archives-ouvertes.fr/hal-00489213
Rigorous Derivation of Incompressible e-MHD Equations from Compressible Euler???Maxwell Equations, SIAM Journal on Mathematical Analysis, vol.40, issue.2, pp.540-565, 2008. ,
DOI : 10.1137/070686056
URL : https://hal.archives-ouvertes.fr/hal-00489212
Relaxation limit and global existence of smooth solutions of compressible Euler-Maxwell equations, SIAM, J. Math. Anal, pp.43-944, 2011. ,
Boundary layers and quasi-neutral limit in steady state Euler???Poisson equations for potential flows, Nonlinearity, vol.17, issue.3, pp.835-849, 2004. ,
DOI : 10.1088/0951-7715/17/3/006
Convergence of compressible Euler-Poisson equations to incompressible type Euler equations, Asymptotic Anal, pp.41-141, 2005. ,
Global Solutions to the Isothermal Euler-Poisson System with Arbitrarily Large Data, Journal of Differential Equations, vol.123, issue.1, pp.123-193, 1995. ,
DOI : 10.1006/jdeq.1995.1158
Introduction to Ionospheric Physics, 1969. ,
Stabilité d'un plasma : modélisation mathématiques et simulation numérique, 1994. ,
The incompressible limit and the initial layer of the compressible Euler equation, Journal of Mathematics of Kyoto University, vol.26, issue.2, pp.323-354, 1986. ,
DOI : 10.1215/kjm/1250520925
Quasineutral Limit of Euler???Poisson System with and without Viscosity, Communications in Partial Differential Equations, vol.157, issue.3-4, pp.29-419, 2004. ,
DOI : 10.1081/PDE-120030403
Relaxation-time limits of non-isentropic hydrodynamic models for semiconductors, Journal of Differential Equations, vol.247, issue.6, pp.1777-1795, 2009. ,
DOI : 10.1016/j.jde.2009.06.018
The non-relativistic limit of Euler-Maxwell equations for two-fluid plasma, Nonlinear Anal, TMA, pp.72-1829, 2010. ,
Diffusive Relaxation Limit of Multidimensional Isentropic Hydrodynamical Models for Semiconductors, SIAM Journal on Applied Mathematics, vol.64, issue.5, pp.1737-1748, 2004. ,
DOI : 10.1137/S0036139903427404
Entropy and Global Existence for Hyperbolic Balance Laws, Archive for Rational Mechanics and Analysis, vol.172, issue.2, pp.247-266, 2004. ,
DOI : 10.1007/s00205-003-0304-3
Convergence of the Godunov scheme for a simplified one-dimensional hydrodynamic model for semiconductor devices, Communications in Mathematical Physics, vol.120, issue.3, pp.1-22, 1993. ,
DOI : 10.1007/BF02098016