Globale Existenz und Eindeutigkeit starker Lösungen für ein Gleichungssystem, das den Ladungstransport in einem Halbleiter beschreibt

Abstract

Global existence of strong solutions is shown for a system of differential equations describing carrier transport in semiconductors which up to now has only been known to have weak solutions. At first the proof of existence is carried out for a "small" interval of the time-axis with the help of several imbedding theorems and Banach’s fixed point theorem and then is extended to an arbitrary interval. At last further smoothness properties of the solution are discussed under spezial conditions for initial and boundary values.