Asymptotic Behavior of the Solution to a Nonisentropic Hydrodynamic Model of Semiconductors

We study the asymptotic behavior of the solution for a hydrodynamic model of semiconductors where the energy equation is included. We study the case where the flow is subsonic and the doping profile is close to a negative constant, depending on the spacial variablex. We shall show that a given steady state solution is asymptotically stable or unstable depending on whether or not the density of the initial data satisfiesP=0, wherePis defined in (3.5).