Publication Cover
Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 16
126
Views
2
CrossRef citations to date
0
Altmetric
Articles

Existence and asymptotic behavior of smooth solutions to bipolar hydrodynamic model

&
Pages 2880-2892 | Received 10 Jun 2017, Accepted 12 Oct 2017, Published online: 01 Nov 2017
 

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.

AMS Subject Classifications:

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.

1. In fact, the Fourier series of y and are

The Parseval inequality indicate

2. In fact, the smallness of and indicate | E| and are small. We will use these two facts directly.

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].

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.