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Long-time behavior of solutions to the bipolar hydrodynamic model of semiconductors with boundary effect

Feimin Huang Ming Mei Yong Wang Tong Yang

Analysis of PDEs mathscidoc:1912.43960

SIAM Journal on Mathematical Analysis, 44, (2), 1134-1164, 2012.4
For a bipolar hydrodynamic model of semiconductors in the form of EulerPoisson equations with Dirichlet or Neumann boundary conditions, in this paper we first heuristically analyze the most probable asymptotic profile (the so-called diffusion waves) and then prove this long-time behavior rigorously. For this, we construct correction functions to show the convergence of the original solution to the diffusion wave with optimal convergence rates by the energy method. Moreover, in the case with Dirichlet boundary condition, when the initial perturbation is in some weighted L^1 space, a faster and optimal convergence rate is also given.
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@inproceedings{feimin2012long-time,
  title={Long-time behavior of solutions to the bipolar hydrodynamic model of semiconductors with boundary effect},
  author={Feimin Huang, Ming Mei, Yong Wang, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210921470244524},
  booktitle={SIAM Journal on Mathematical Analysis},
  volume={44},
  number={2},
  pages={1134-1164},
  year={2012},
}
Feimin Huang, Ming Mei, Yong Wang, and Tong Yang. Long-time behavior of solutions to the bipolar hydrodynamic model of semiconductors with boundary effect. 2012. Vol. 44. In SIAM Journal on Mathematical Analysis. pp.1134-1164. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210921470244524.
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