The Existence Of An Energy Transport Model With Large Initial Data

The energy transport models are commonly used to describe the characteristics of charged particle with some important basic particles quantities under the action of electric field,includ-ing the mass conservation equation,energy balance equation,and which can also used to de-scribe the change of the internal temperature of the semiconductor material and the phenomenon of high electric field,etc.Therefore,it is important to study the energy transport models in view of theoretical and practical value.In this dissertation,the global existence of smooth solution-s with large initial data for the one-dimensional energy transport model is studied.The energy transport models can also be derived from non-isentropic Euler-possion equations derived out through the relaxation limit,the proof is based on some detailed analysis on the density and temperature functions.This dissertation is divided into three chapters.The first chapter mainly introduced some researched results energy transport model,the Euler-Possion equations and Navier-Stokes-Possion equations,and we derived the energy transport models in the form of the Lagrangian coordinates.At last,we present the main results.The second chapter is mainly list some inequal-ities and theorems,which will be use in this dissertation.The third chapter is a prior estimate.The main content of this chapter is the proof of the theorem 1.1.The first part of this chapter is the local existence of the energy transport model,then we introduce some convex entropy func-tions to obtain of basic energy estimates by the time for partial derivative.The second part is to obtained the bounds of the energy transport model solutions.Firstly,we estimate a lower bound v/T in terms of the lower bound of v by the standard maximum principle of parabolic equation.Secondly,with the help of the analysis of T/v and its derivatives,combining Sobolev embedding theorem and literature[33]the Y.k anel method to the upper and lower bounds of the energy transport model solutions.