Large Time Behavior Of Initial-boundary Value Problem Of The One-dimensional Hyperbolic-elliptic Coupled Equations In Radiating Gas

This thesis is concerned with the study of the large time behavior of the initial-boundary value problem on the half line for a one-dimensional hyperbolic-elliptic coupled equations in radiating gas,which is a system coupled by the classic com-pressible non-isentropic Euler equations with an elliptic equation.We are devoted to the case when the velocity of the inward flow on the boundary is given as a positive constant.The asymptotic stability of the rarefaction wave without restrictions on the smallness of the wave strength is proved,provided that the data on the bound-ary is supersonic.It is an improved result on the initial-boundary value problem for the hyperbolic-elliptic coupled equations in radiating gas.Compared to existing result,we obtain global existence under the assumption that initial data are required lower regularities.In addition,we also improve the regularities by imposing more regularities on initial data.This thesis consists of five chapters.They are written by:Chapter one:In this chapter,we present the hyperbolic-elliptic coupled equation in radiating gas,and propose our problems.Then we review some existing results related to our problem.Chapter two:In this chapter,we first recall fundamental theory of hyperbol-ic conservation laws.Then the Riemann problem of viscous Burgers equations is introduced.Properties of smooth rarefaction waves are constructed based on the Riemann problem of non-isentropic Euler equations.The main theorem of this the-sis are given.Chapter three:In this chapter,we reformulate the problem and establish the local-in-time existence of the reformulated problem.Chapter four:In this chapter,we prove series of a priori estimates under the assumption of lower regularities on initial data.And the global-in-time existence can be established with a priori estimates and then the first theorem is proved,and this improves previous result.Chapter five:In this chapter,we improved regularities by imposing more regu-larities on initial data,and the second theorem is proved.