On the Semiconductor System (Journal of Partial Differential Equations, 1992)
In this paper, the semiconductor system is discussed. The existence and uniqueness or the global solution or the carrier transport problem are obtained. Under the condition that the width in some direction of the domain being sufficiently small, the existence and uniqueness of the solution of the steady states are proved. It is also proved that the solution of the carrier transport problem tends to the solution or the steady states problem exponentially when t goes to infinity.