Existence and asymptotic behavior of smooth solutions to bipolar hydrodynamic model

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.

Keywords:

• Hydrodynamic model
• bipolar semiconductor device
• stationary solution
• smooth solutions
• asymptotic behavior

AMS Subject Classifications:

• 35L02
• 35L60

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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Additional information

Funding

This project is supported in part by the National Natural Science Foundation of China [grant number 11541005], [grant number 11671237]; Shandong Provincial Natural Science Foundation [grant number ZR2015AM001].