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Asymptotic stability of nonlinear diffusion waves for the bipolar quantum Euler-Poisson system with time-dependent damping.
  • Qiwei Wu,
  • Xiaofeng Hou
Qiwei Wu
Shanghai University

Corresponding Author:wuqiwei_shu@163.com

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Xiaofeng Hou
Shanghai University
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Abstract

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 $\frac{J_i}{(1+t)^{\lambda}}(i=1,2)$ 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.
31 May 2022Submitted to Mathematical Methods in the Applied Sciences
02 Jun 2022Submission Checks Completed
02 Jun 2022Assigned to Editor
06 Jun 2022Reviewer(s) Assigned
14 Sep 2022Review(s) Completed, Editorial Evaluation Pending
26 Sep 2022Editorial Decision: Revise Minor
28 Sep 20221st Revision Received
28 Sep 2022Submission Checks Completed
28 Sep 2022Assigned to Editor
06 Oct 2022Reviewer(s) Assigned
07 Oct 2022Review(s) Completed, Editorial Evaluation Pending
11 Oct 2022Editorial Decision: Accept