Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation

We investigate the relaxation problem for the hydrodynamic isentropic Euler-Poisson system when the momentum relaxation time tends to zero. Very sharp estimates on the solutions, independent of the relaxation time, are obtained and used to establish compactness.

[1]  Peizhu Luo,et al.  CONVERGENCE OF THE LAX–FRIEDRICHS SCHEME FOR ISENTROPIC GAS DYNAMICS (III) , 1985 .

[2]  Pierangelo Marcati,et al.  The One-Dimensional Darcy's Law as the Limit of a Compressible Euler Flow , 1990 .

[3]  W. V. Roosbroeck.  Theory of the flow of electrons and holes in germanium and other semiconductors , 1950 .

[4]  C. D. Levermore,et al.  Hyperbolic conservation laws with stiff relaxation terms and entropy , 1994 .

[5]  Luc Tartar,et al.  Compensated compactness and applications to partial differential equations , 1979 .

[6]  C. Schmeiser,et al.  Semiconductor equations , 1990 .

[7]  J. Smoller.  Shock Waves and Reaction-Diffusion Equations , 1983 .

[8]  Bo Zhang,et al.  Convergence of the Godunov scheme for a simplified one-dimensional hydrodynamic model for semiconductor devices , 1993 .

[9]  P. Lax.  Weak solutions of nonlinear hyperbolic equations and their numerical computation , 1954 .

[10]  R. J. DiPerna.  Convergence of approximate solutions to conservation laws , 1983 .

[11]  Anile,et al.  Thermodynamic derivation of the hydrodynamical model for charge transport in semiconductors. , 1992, Physical review. B, Condensed matter.

[12]  Pierangelo Marcati,et al.  Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system , 1988 .

[13]  R. J. Diperna,et al.  Convergence of the viscosity method for isentropic gas dynamics , 1983 .

[14]  Irene M. Gamba.  Stationary transonic solutions of a one—dimensional hydrodynamic model for semiconductors , 1992 .

[15]  F. Poupaud,et al.  Global Solutions to the Isothermal Euler-Poisson System with Arbitrarily Large Data , 1995 .

[16]  Uri M. Ascher,et al.  A PHASE PLANE ANALYSIS OF TRANSONIC SOLUTIONS FOR THE HYDRODYNAMIC SEMICONDUCTOR MODEL , 1991 .

[17]  Massimo Rudan,et al.  MULTI‐DIMENSIONAL DISCRETIZATION SCHEME FOR THE HYDRODYNAMIC MODEL OF SEMICONDUCTOR DEVICES , 1986 .

[18]  I. Bohachevsky,et al.  Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics , 1959 .

[19]  G. Baccarani,et al.  An investigation of steady-state velocity overshoot in silicon , 1985 .

[20]  A non‐isentropic Euler–Poisson model for a collisionless plasma , 1993 .

[21]  Gui-Qiang G. Chen,et al.  Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics , 1989 .

[22]  A. M. Anile,et al.  Extended thermodynamics of the Blotekjaer hydrodynamical model for semiconductors , 1992 .

[23]  Gui-Qiang G. Chen,et al.  Zero relaxation and dissipation limits for hyperbolic conservation laws , 1993 .

[24]  F. Poupaud.  Derivation of a hydrodynamic system hierarchy for semiconductors from the Boltzmann equation , 1991 .