Stability of Steady State Solutions for an Isentropic Hydrodynamic Model of Semiconductors of Two Species

We discuss the stability of the steady state solutions for an isentropic hydrodynamic model of semiconductors of two species. We consider not only the mass and momentum equations for electrons, but also those two equations for holes. The recombination effects between electrons and holes are taken into consideration as well. We study the case where the doping profile is close to zero and depends on the spacial variable x. We shall show that steady state solutions are asymptotically stable.