具有某种源气体动力学方程组定解问题整体解的渐近性

THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A CLASS OF INHOMOGENEONS SYSTEMS OF GAS DYNAMICS

对于方程组(1.1)的齐次形式(f(u)=0),Kazhikhov 证明了初边值问题(1.1)—(1.3)的解的整体存在性以及渐近性.随后,陈贵强、陆云光对于非齐次方程组(1.1)的初边值问题的解的整体存在性给予了证明.本文研究方程组(1.1)的初边值问题整体解的渐近性.

Consider an initial-boundary problemv_t-u_x=0,u_t+((aθ)/v)_x+f(u)=((μu_x)/v)_x,θ_t+(aθ)/v u_x=((kθ_x)/v)_x+(μu_x)/v,(E)v(x,0)=v_0(x),u(x,0)=u_0(x),θ(0,x)=θ_0(x),(I)u(t,0)=u(t,1)=θ_x(t,0)=θ_x(t,1).(J)Sufficient and necessary conditions for (E),(I),(J) to have asymptotic stability ofthe gobal smooth solution are givens by means of the elemental L^2 energy method.