Abstract
An analysis of asymptotic wave solutions for the hydrodynamical model of semiconductors based on Extended Thermo-dynamics [1, 2, 3, 4] is presented. The evolution equations form a quasilinear hyperbolic system, coupled to the Poisson equation for the electric potential. The aim of this article is to describe the far field for such a model by a suitable adaptation of the asymptotic expansion proposed in [5, 6, 7]. The stationary solution for uniformly doped semiconductor has been taken as unperturbed state. We distinguish two cases: perturbations with wavelength smaller than the scaled Debye length and perturbations of the same order of the Debye length. In the first case the perturbation of the electric field is negligible and the resulting model equation exhibits nonlinear and relaxation effects. In the second case a drift term due to the presence of a non negligible perturbation of the electric field arises as well.
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