Large-time behavior of solutions to bipolar Euler-Poisson equations with time-dependent damping in the half space

Abstract

This paper is concerned with the large-time behavior of solutions to an initial boundary value problem for the one-dimensional bipolar Euler-Poisson equations with time-dependent damping effects Ji(1+t)λ(i=1,2) for −1<λ<1. We first show the decay rates of the corresponding asymptotic profiles, the so-called nonlinear diffusion waves, then by means of the time-weighted energy method, we prove that the smooth solutions to the initial-boundary value problem exist uniquely and globally, and time-asymptotically converge to the nonlinear diffusion waves, provided that the initial perturbation around the diffusion wave is small enough. The convergence rates are in the forms that O(t−34(1+λ)) for −1<λ<35 and O(tλ−32) for 35<λ<1, respectively, where λ=35 is the critical point, and the convergence rate at the critical point is O(t65lnt). The results are different from those of the Cauchy problem in Li et al. (2019) [20].