Asymptotic stability of nonlinear diffusion waves for the bipolar quantum Euler–Poisson system with time‐dependent damping

摘要

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 −Ji(1+t)λ(i=1,2)$$ -frac{J_i}{{left(1#x0002B;tright)}#x0005E;{lambda }}left(i#x0003D;1,2right) $$ for −1<λ<1$$ -1lambda 1 $$. 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 wave.