Pointwise estimates and Lp convergence rates to diffusion waves for a one-dimensional bipolar hydrodynamic model

In this paper, we study the stability of the diffusion wave to the one-dimensional hydrodynamic model, which takes the bipolar Euler-Poisson system with relaxation effect. The pointwise estimate of the smooth solutions is obtained by the weighted energy method and the approximate Green function when the initial perturbations are sufficiently small. Based on it, we further achieve the optimal time decay rate of the solutions in Lp(1≤p≤+∞). It coincides with the time decay rate of the solution in Gasser et al. (2003).