Abstract
The initial value problem is considered in the present paper for the bipolar quantum hydrodynamic (QHD) model for semiconductors in ℝ3. 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Mathematical Models and Methods in Applied Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
