Relaxation Time Limits Of Bipolar Non-isentropic Euler-Poisson Equations

In this paper,the large-time asymptotic behavior of bipolar Non-isentropic Euler-Poisson equation system and the relaxation time limit of smooth solution of the model are studied.The model is coupled with Euler equation and Poisson equation.The relationship between the smooth solution of the model,the energy transport model and the drift-diffusion model under different relaxation time limits is obtained.The uniform energy estimates for relaxation time are obtained by constructing appropriate energy functional.Secondly,the smooth solutions of bipo-lar Non-isentropic Euler-Poisson equations converge to the solutions of energy transport model and drift diffusion model respectively at different time scales by using compactness analysis.The structure of this paper is as follows:In the first chapter,the research background of the model and the main research status at home and abroad are briefly introduced.Finally,the bipolar Non-isentropic Euler-Poisson equations are introduced and the main research conclusions of this paper are given.In the second chapter,the important inequalities and the theorems used in the research are given.In Chapter 3,the uniform priori estimates of relaxation time for smooth solutions of bipo-lar Non-isentropic Euler-Poisson equations are established.Firstly,by constructing appropriate energy functional,the uniform priori estimates of relaxation time for smooth solutions are ob-tained in two steps.By constructing zero-order and first-order energy density functional,we get the priori estimates of smooth solutions in the sense of H~1.Then the energy density functional of higher order(2 order and 3 order)is constructed to obtain a priori estimate of relaxation time for smooth solutions.In Chapter 4,the relaxation time limit of the smooth solution model of this bipolar Non-isentropic Euler-Poisson equation system is studied.Under different relaxation time limits,the smooth solution converges to the solution of the energy transport model and the drift diffusion model respectively,and the convergence of the solution is obtained.