In this project a one-dimensional isentropic version of the hydro-dynamic model for semiconductors will be
studied. In particular, the asymptotic behaviour of solutions for long times and as the momentum relaxation time
tends to zero will be investigated. Existing results will be extended to the case of a non-constant relaxation time
and/or to problems with boundaries. The methodology includes the shifted-weighted energy method for the long
time asymptotics as well as compensated compactness for the zero relaxation time limit.