In this paper, we investigate the global existence and large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Possion equations with time and spacedependent damping in a bounded interval. Firstly, we prove the existence of entropy solutions through vanishing viscosity method and compensated compactness framework. Based on the uniform estimates of density, we then prove the entropy solutions converge to the corresponding unique stationary solution exponentially with time. We generalize the existing results to the variable coefficient damping case.

中文翻译：

---

变系数阻尼半导体器件一维单极水动力模型熵解的存在性和长时间行为

在本文中，我们研究了一维单极流体动力学模型的熵解的全局存在性和长时间行为，该熵解的存在时间和空间依赖于有界区间的Euler-Possion方程形式。首先，我们通过消失粘度法和补偿紧致度框架证明了熵解的存在。基于密度的均匀估计，然后证明熵解随时间呈指数收敛到相应的唯一平稳解。我们将现有结果推广到变系数阻尼情况。