Combined relaxation and non-relativistic limit of non-isentropic Euler–Maxwell equations

Abstract

This paper is devoted to study the combined relaxation and non-relativistic limit of non-isentropic Euler–Maxwell equations with relaxation for semiconductors and plasmas. We prove that, as the relaxation time tends to zero and the light speed tends to infinite, periodic initial-value problem of a certain scaled non-isentropic Euler–Maxwell equations has unique smooth solution existing in the time interval where the corresponding classical driftdiffusion model has smooth solutions. It is shown that the relaxation regime plays a decisive role in the combined limit. Furthermore, the corresponding convergence rate is obtained.

Keywords:

• non-isentropic Euler–Maxwell equations
• relaxation limit
• non-relativistic limit
• drift-diffusion model

AMS Subject Classifications:

• 35B40
• 35L60
• 35Q35

Acknowledgments

The author would like to thank the referees for useful comments to improve the presentation of this paper.

Additional information

Funding

This research was supported by the Joint Funds of the National Natural Science Foundation of China [grant number U1204103], China Postdoctoral Science Foundation Funded Project (No.: 2013M530032) and the science and technology research projects of Education Department of Henan province [grant number 13A110731].