On Weak Solutions to the Non-stationary van Roosbroeck's System with Discontinuous Permittivities

Abstract

In this paper we prove the existence of a weak solution to the non-stationary drift–diffusion equations (van Roosbroeck's system) of semiconductor theory involving discontinuous permittivities. The proof is based on an approximation of these equations by a system with bounded non-linearities, deriving a priori estimates on the approximate solutions and then carrying out the passage to limit. The discussion is completed by some regularity results for the weak solution under consideration. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 689–706 (1997).