Large Time Behavior of the Solutions to a Hydrodynamic Model for Semiconductors
Large Time Behavior of the Solutions to a Hydrodynamic Model for Semiconductors
复制标题
DOI：
10.1137/s0036139996312168
复制
发表时间：
1998-12
期刊：
影响因子：
--
通讯作者：
R. Natalini;T. Luo;Z. Xin
中科院分区：
文献类型：
--
作者：
R. Natalini;T. Luo;Z. Xin
我们建立了小初值下一维半导体等熵Euler-Poisson（或流体动力学）模型Cauchy问题整体光滑解的存在性。特别是，我们表明，作为$t\\infty$，这些解决方案收敛到固定的漂移扩散方程的解决方案。在不作小性假设的情况下，证明了漂移扩散方程平稳解的存在唯一性。
We establish the global existence of smooth solutions to the Cauchy problem for the one-dimensional isentropic Euler--Poisson (or hydrodynamic) model for semiconductors for small initial data. In particular we show that, as $t\to\infty$, these solutions converge to the stationary solutions of the drift-diffusion equations. The existence and uniqueness of stationary solutions to the drift-diffusion equations are proved without the smallness assumption.