Asymptotic stability of a stationary solution for the bipolar full Euler–Poisson equation in a bounded domain

Abstract

In this paper, we present a bipolar full hydrodynamic model from semiconductor devices, which takes the form of bipolar full Euler–Poisson with electric field and relaxation terms added to the momentum equations and energy equations. We firstly prove the existence of the stationary solutions under proper boundary value conditions. Next, we present the global existence and the asymptotic behavior of smooth solutions to the initial boundary value problem for the one-dimensional bipolar full Euler–Poisson system in a bounded domain. The result is shown by an elementary energy method. Compared with the corresponding initial data case, we find that the asymptotic state of the solutions is the stationary solution.