In this paper, we study the zero relaxation time limits to a one dimensional hydrodynamic model of two carrier types for semiconductors. First, we introduce the flux approximation coupled with the classical viscosity method to obtain the uniform $$L_{loc}^{p}, p \ge 1, $$ bound of the approximation solutions $$ \rho _{i}^{ \varepsilon ,\delta } $$ and other estimates of $$ (u_{i}^{ \varepsilon ,\delta }, E^{ \varepsilon ,\delta })$$ with the help of the high energy estimates (Jungel and Peng Comm Partial Differ Equ 58:1007–1033, 1999). Then, we apply the compensated compactness method coupled with the scaled variables technique (Marcati and Natalini Arch Ration Mech Anal 129:129–145, 1995) to prove the zero-relaxation-time limits with arbitrarily large initial data, and arbitrary adiabatic exponents $$ \gamma _{i} > 1$$ .

中文翻译：

---

半导体的两种载流子类型的流体动力学模型的零弛豫时间限制

在本文中，我们研究了半导体的两种载流子类型的一维流体动力学模型的零弛豫时间限制。首先，我们引入通量近似与经典粘度方法相结合，以获得近似解的统一 $$L_{loc}^{p}, p \ge 1, $$ bound $$ \rho _{i}^{ \varepsilon ,\delta } $$ 和 $$ (u_{i}^{ \varepsilon ,\delta }, E^{ \varepsilon ,\delta })$$ 的其他估计值，在高能量估计值的帮助下（Jungel和 Peng Comm Partial Differ Equ 58:1007–1033, 1999)。然后，我们应用补偿紧致度方法与缩放变量技术（Marcati 和 Natalini Arch Ration Mech Anal 129:129–145, 1995）来证明具有任意大初始数据和任意绝热指数的零松弛时间限制 $ $ \gamma _{i} > 1$$ 。