Convergence of the nonisentropic Euler–Poisson equations to incompressible type Euler equations

In this paper, we investigate a multidimensional nonisentropic hydrodynamic (Euler–Poisson) model for semiconductors. We study the convergence of the nonisentropic Euler–Poisson equation to the incompressible nonisentropic Euler type equation via the quasi-neutral limit. The local existence of smooth solutions to the limit equations is proved by an iterative scheme. The method of asymptotic expansion and energy methods are used to rigorously justify the convergence of the limit.