Asymptotic stability of nonlinear diffusion waves for the bipolar
quantum Euler-Poisson system with time-dependent damping.
We shall investigate the asymptotic behavior of solutions to the Cauchy
problem for the one-dimensional bipolar quantum Euler-Poisson system
with time-dependent damping effects
for $-1<\lambda<1$. Applying the
technical time-weighted energy method, we prove that the classical
solutions to the Cauchy problem exist uniquely and globally, and
time-algebraically converge to the nonlinear diffusion waves. This study
generalizes the results in [Y.-P. Li, Nonlinear Anal., 74(2011),
1501-1512] which considered the bipolar quantum Euler-Poisson system
with constant coefficient damping.