J. Frehse et J. Naumann, ON THE EXISTENCE OF WEAK SOLUTIONS TO A SYSTEM OF STATIONARY SEMICONDUCTOR EQUATIONS WITH AVALANCHE GENERATION, Mathematical models and methods in applied sciences, 4(2), 1994, pp. 273-289
This paper is concerned with the stationary drift-diffusion equations
of semiconductor theory involving recombination-generation of carriers
due to particle transition, and pure generation by impact ionization
(avalanche generation). We establish the existence of a weak solution
to the mixed boundary value problem for the system of PDEs under consi
deration. In the proof we combine an approximation argument with some
estimates based on a positivity property of the recombination-generati
on term.