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In the paper, we consider a multi-dimensional bipolar hydrodynamic model fromsemiconductor devices and plasmas. This system takes the form of Euler-Poissonwith electric field and frictional damping added to the momentum equations. Weshow the global existence and $L^{p}$ convergence rates of planar diffusionwaves for multi-dimensional bipolar Euler-Poisson systems when the initial dataare near the planar diffusive waves. A frequency decomposition and approximateGreen function based on delicate energy method are used to get the optimaldecay rates of the planar diffusion waves. To our knowledge, the$L^p(p\in[2,+\infty])$-convergence rate of planar waves improves the previousresults about the $L^2$-convergence rates.

Global existence and $L^{p}$ convergence rates of planar waves for three-dimensional bipolar Euler-Poisson systems