Asymptotic convergence to planar stationary waves for multi-dimensional unipolar hydrodynamic model of semiconductors

In this study, we consider the high dimensional unipolar hydrodynamic model for semiconductors in the form of Euler–Poisson equations. Based on the results that we have obtained in the first part (Huang, et al., 2011 [16]) for the 1-D case, we can further show the stability of planar stationary waves in multi-dimensional case. Utilizing the energy method, we obtain the global existence of the solutions of high dimensional Euler–Poisson equations for the unipolar hydrodynamic model, and prove that the solutions converge to the planar stationary waves time-exponentially.