This paper is concerned with the Cauchy problem of a bipolar hydrodynamic model for semiconductor device, a system of one dimensional Euler–Poisson equations with time-dependent damping effect in the critical case. The global existence and uniqueness of the solutions to the Cauchy problem are proved by the technical time-weighted energy method, when the initial perturbation around the constant states are small enough. Particularly, the algebraic time-convergence-rates for the solutions to their constant states are also derived.

中文翻译：

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临界情况下具有瞬态阻尼的双极欧拉-泊松系统柯西问题解的大时间行为

本文关注半导体器件双极流体动力学模型的柯西问题，这是一个在临界情况下具有瞬态阻尼效应的一维 Euler-Poisson 方程组。当恒定状态周围的初始扰动足够小时，柯西问题解的全局存在性和唯一性通过技术时间加权能量方法证明。特别是，还推导出了其恒定状态解的代数时间收敛率。