Stability Of Rarefaction Waves For Hyperbolic-elliptic Coupled System

In this paper, we will study the Cauchy problem for a model of hyperbolic-elliptic coupled system derived from approximating the one-dimensional system of the radiating gas. When initial data is a small disturbance of rarefaction wave of inviscid Burgers equation, we prove the global existence of the solution to the corresponding Cauchy problem and asymptotic stability of rarefaction wave. The analysis is based on a priori estimates and L²-energy method.In chapter one, we introduce the model of hyperbolic-elliptic coupled system derived from approximating the one-dimensional system of the radiating gas.In chapter two, we give the smooth approixmation and preliminaries.In chapter three, we give the proof of the main theorem. we state our main results as follows:Theorem 2.2. Let w₀∈H²(R) andε₀ = ||w₀||₂² andδ= |u₊－u_-| are sufficiently small. Then the Cauchy problem (1.1), (1.2) (or equivalently (2.6), (2.7)) admits a unique global solution (w(x,t),z(x,t))∈X(0,T) satisfyingwhereMoreover...