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

Article type: Research Article

Authors: Naumann, J.

Affiliations: Institut für Angewandte Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany

Note: [] Correspondence to: J. Naumann, Institut für Angewandte Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany.

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.

DOI: 10.3233/ASY-1995-11104

Journal: Asymptotic Analysis, vol. 11, no. 1, pp. 55-72, 1995