Relaxation time limits problem for hydrodynamic models in semiconductor science*

In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler–Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.