Abstract
<p style='text-indent:20px;'>We shall investigate the large-time behavior of solutions to the Cauchy problem for the one-dimensional bipolar quantum Euler-Poisson system with critical time-dependent over-damping. By means of the time-weighted energy method, we prove that the smooth solutions to the Cauchy problem exist uniquely and globally, and time-asymptotically converge to the nonlinear diffusion waves when the initial perturbation around the nonlinear diffusion waves are small enough. Particularly, we show the optimal decay rates of solutions toward the nonlinear diffusion waves.</p>
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