Date of Graduation
In this thesis we study two cases of the hydrodynamic model of semiconductors: the nonisentropic case for one species and the isentropic case for two species. The purpose of this thesis is to discuss the asymptotic stability of the steady state solutions for these two cases. First we show the existence of a one-parameter family of steady state solutions. Each steady state solution is uniquely determined by the momentum. Then, we prove that every steady state solution is asymptotically stable. Namely, if the initial data is "close" to a given steady state solution, then the dynamic solution will asymptotically approaches to this steady state solution as time goes to the infinity. Moreover, in the case that the initial data is not "close" to a given steady state solution, we shall provide a simple mechanism to find out another steady state solution to which the dynamic solution asymptotically approaches. The definition for "closeness" is given in subsection 2.3 and 3.3 in this thesis.
Zhu, Chen, "Mathematical analysis for the hydrodynamic model of semiconductors." (1997). Graduate Theses, Dissertations, and Problem Reports. 10115.