Relaxation limit and initial layer analysis of a bipolar hydrodynamic model for semiconductors

This paper is concerned with a bipolar hydrodynamical model for semiconductors or plasma with short momentum relaxation time in several space variables. We first construct formal approximations of the initial layer solution to the nonlinear problem by the matched expansion method. Then, assuming some regularity of the solution to the reduced problem and using the energy method, we prove the global existence of classical solutions, and justify the validity of the formal approximations in any fixed compact subset of the uniform time interval and give the convergence rate up to any order.