An existence theorem for weak solutions of the semiconductor equations modelling the non-stationary avalanche generation

Abstract

The paper is concerned with the non-stationary semiconductor equations (van Roosbroeck's system) involving a gradient non-linearity which models the generation of particles due to impact ionization. We establish the existence of a weak solution to this system over a cylinder Ω×(0,T₁) (Ω⊂R² bounded domain, (0, T₁) small time interval). The method of proof relies on approximating the generation term by bounded gradient non-linearities.