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On steady state Euler-Poisson models for semiconductors

  • Peter A. Markowich
Original Papers

Abstract

This paper is concerned with an analysis of the Euler-Poisson model for unipolar semiconductor devices in the steady state isentropic case. In the two-dimensional case we prove the existence of smooth solutions under a smallness assumption on the prescribed outflow velocity (small boundary current) and, additionally, under a smallness assumption on the gradient of the velocity relaxation time. The latter assumption allows a control of the vorticity of the flow and the former guarantees subsonic flow. The main ingredient of the proof is a regularization of the equation for the vorticity.

Also, in the irrotational two- and three-dimensional cases we show that the smallness assumption on the outflow velocity can be replaced by a smallness assumption on the (physical) parameter multiplying the drift-term in the velocity equation. Moreover, we show that solutions of the Euler-Poisson system converge to a solution of the drift-diffusion model as this parameter tends to zero.

Keywords

Steady State Vorticity Smooth Solution Semiconductor Device Main Ingredient 
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References

  1. [1]
    P. A. Markowich, C. Ringhofer and C. Schmeiser,Semiconductor Equations, Springer Verlag, Wien-New York 1990.Google Scholar
  2. [2]
    P. A. Markowich and P. Degond,On a one-dimensional hydrodynamic model for semiconductors, Appl. Math. Letters3, 25–29 (1990).Google Scholar
  3. [3]
    P. A. Markowich and P. Degond,A steady state potential flow model for semiconductors, to appear in Ann. Scuola Sup. e Norm. di Pisa (1991).Google Scholar
  4. [4]
    David Gilbarg and Neil S. Trudinger,Elliptic Partial Differential Equations of Second Order, 2nd Ed. Springer-Verlag, Berlin 1983.Google Scholar
  5. [5]
    F. Brezzi and G. Gilardi,Fundamentals of P.D.E. for numerical analysis, Report Nr. 446, Inst. di Analisi Numerici, Univ. di Pavia, Italy (1984).Google Scholar
  6. [6]
    D. R. Smart,Fixed Point Theorems, Cambridge University Press 1974.Google Scholar

Copyright information

© Birkhäuser Verlag 1991

Authors and Affiliations

  • Peter A. Markowich
    • 1
  1. 1.Dept of MathematicsPurdue UniversityWest LafayetteUSA

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