zbMATH — the first resource for mathematics

On steady state Euler-Poisson models for semiconductors. (English) Zbl 0755.35138
(Author’s summary.) 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 shift-diffusion model as this parameter tends to zero.

35Q60 PDEs in connection with optics and electromagnetic theory
35Q35 PDEs in connection with fluid mechanics
35B65 Smoothness and regularity of solutions to PDEs
Full Text: DOI
[1] P. A. Markowich, C. Ringhofer and C. Schmeiser,Semiconductor Equations, Springer Verlag, Wien-New York 1990.
[2] P. A. Markowich and P. Degond,On a one-dimensional hydrodynamic model for semiconductors, Appl. Math. Letters3, 25-29 (1990). · Zbl 0736.35129
[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). · Zbl 0808.35150
[4] David Gilbarg and Neil S. Trudinger,Elliptic Partial Differential Equations of Second Order, 2nd Ed. Springer-Verlag, Berlin 1983. · Zbl 0562.35001
[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).
[6] D. R. Smart,Fixed Point Theorems, Cambridge University Press 1974. · Zbl 0297.47042
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.