Asymptotic stability of a stationary solution to a hydrodynamic model of semiconductors. (English) Zbl 1138.82033

The paper is concerned with the existence of the stationary solution and asymptotic stability properties of solutions to a hydrodynamic system of partial differential equations, devised to describe the motion of electrons in semiconductors. A mathematical survey of this issue can be found in the monograph “Semiconductor equations” by P. A. Markowich, C. A. Ringhofer and C. Schmeiser [Berlin: Springer-Verlag (1990; Zbl 0765.35001)]. Departing from earlier discussions of transport of electrons in semiconductors and the inferred one-dimensional steady state hydrodynamic model, the present paper addresses an issue of the existence and the asymptotic stability of its solutions, without specific demands concerning the so-called doping profile.


82D37 Statistical mechanics of semiconductors
76E99 Hydrodynamic stability
76N99 Compressible fluids and gas dynamics
35L50 Initial-boundary value problems for first-order hyperbolic systems
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation


Zbl 0765.35001
Full Text: Euclid


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