Algebraic time decay for the bipolar quantum hydrodynamic model

作者：Li Hai Liang^*; Zhang Guojing; Zhang Kaijun

来源：Mathematical Models and Methods in Applied Sciences, 2008, 18(6): 859-881.

DOI：10.1142/S0218202508002887

• quantum hydrodynamics
• algebraic time decay rate

The initial value problem is considered in the present paper for the bipolar quantum hydrodynamic (QHD) model for semiconductors in R-3. The unique strong solution exists globally in time and tends to the asymptotical state with an algebraic decay rate as time goes to infinity is proved. And, the global solution of linearized bipolar QHD system decays in time at an algebraic decay rate from both above and below is shown. This means that in general we cannot get an exponential time-decay rate for bipolar QHD system, which is different from the case of unipolar QHD model ( where global solutions tend to the equilibrium state at an exponential time-decay rate) and is mainly caused by the nonlinear coupling and cancelation between two carriers. Moreover, it is also shown that the nonlinear dispersion does not affect the long time asymptotic behavior, which by product gives rise to the algebraic time-decay rate of the solution of the bipolar hydrodynamical model in the semiclassical limit.

• 出版日期2008-6
• 单位哈尔滨工业大学; 首都师范大学; 东北师范大学