Relaxation-time limit in the multi-dimensional bipolar nonisentropic Euler–Poisson systems

In this paper, we consider the multi-dimensional bipolar nonisentropic Euler–Poisson systems, which model various physical phenomena in semiconductor devices, plasmas and channel proteins. We mainly study the relaxation-time limit of the initial value problem for the bipolar full Euler–Poisson equations with well-prepared initial data. Inspired by the Maxwell iteration, we construct the different approximation states for the case τσ=1τσ=1 and σ=1σ=1, respectively, and show that periodic initial-value problems of the certain scaled bipolar nonisentropic Euler–Poisson systems in the case τσ=1τσ=1 and σ=1σ=1 have unique smooth solutions in the time interval where the classical energy transport equation and the drift-diffusive equation have smooth solution. Moreover, it is also obtained that the smooth solutions converge to those of energy-transport models at the rate of τ2τ2 and those of the drift-diffusive models at the rate of τ, respectively. The proof of these results is based on the continuation principle and the error estimates.