ABSTRACT
We are interested in the existence and asymptotic behavior of smooth solutions to the hydrodynamic model of semiconductors with non-zero doping profile. Within the insulating boundary conditions, recently, a steady state for any doping profile with large amplitude was obtained by using the calculus of variations. In this paper, the obtained steady state is regarded as the background solution. Utilizing energy methods and entropy analysis, we prove the existence of smooth solutions to the hydrodynamic model. As a by-product, we show the smooth solution convergent to the background solution with exponential decay rate.
Acknowledgements
The authors would like to thank Professors Feimin Huang, Ronghua Pan, and Yi Wang for their kindly suggestions and comments.
Notes
No potential conflict of interest was reported by the authors.
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