Global existence and asymptotic behavior of solutions to the nonisentropic bipolar hydrodynamic models

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Li, Yeping

关键词: Bipolar hydrodynamic model;    Diffusive wave;    Smooth solution;    Energy estimates;   

DOI  :  10.1016/j.jde.2010.08.018

来源: Elsevier

【 摘 要 】

In this paper, we consider a one-dimensional bipolar nonisentropic hydrodynamical model from semiconductor devices. This system takes the nonisentropic Euler-Poisson form with electric field and frictional damping added to the momentum equations. First, we prove global existence of smooth solutions to the Cauchy problem. Next, we also discuss the asymptotic behavior of the smooth solutions. We find that in large time, the densities of electron and hole tend to the same nonlinear diffusive wave, the momentums tend to the Darcy's law, and the temperatures tend to the ambient device temperature. Finally, we can obtain the algebraic decay rate of the densities to the same nonlinear diffusive wave, the momentums to the Darcy's law and the temperatures to the ambient device temperature, and the exponential decay of their difference and the electric field to zero. We can show our results by precise energy methods. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free