Stability Of Rarefaction Wave To The 1-dimensional Viscous And Heat-conductive Equations For Reactive Flows

In this paper,we consider the viscous and heat-conductive equations for reactive flows^[31],which can be used to describe the law of flows motion with chemical reaction?such as combustion?in the process of flow and is widely used in aerospace,aerodynamics,material science,etc..We analyse the nonlinear stability of the rarefaction waves through the energy method where the adiabatic constant ??1.Specifically,for the ??1,the weak solution of the viscous and heat-conductive equations for reactive flows?v,u,s,Z? converges to(?V^R,U^R,S^R,0?,when t??,where?V^R,U^R,S^R?is the rarefaction wave of the compressible Euler equations corresponding to the viscous and heat-conductive equations for reactive flows with the mass fraction Z?0.This paper organized as follows:Section 1 is devoted to the background and research progress,we also summarize the main work of this study and the difficulties encountered in the process of proof.In Section 2,we present some special symbols and important inequalities that are used in the proof,we also describe the rarefaction waves for Euler system and the prop-erties for its smooth approximation wave.In Section 3,we use the energy method to prove the nonlinear stability for the viscous and heat-conductive equations for reactive flows about rarefaction waves under the assumption ??1.