数学物理学报(英文版) ›› 1992, Vol. 12 ›› Issue (2): 130-138.
胡家信
Hu Jiaxin
摘要: In this paper we have obtained the existence of weak solutions of the small disturbance equations of steady two-dimension flow
vt-ux=0 ut-(cv2)x=0,(x,t)∈RxR+,with Riemann date
(v(x,0),u(x,0)=(v-,u-),x<0 (v+,u+),x>0 where v+ ≥ 0, v- ≥ 0 and u- ≤ u+ by introducing "artificial" viscosity terms and employing Helley's theorem. The setting under our consideration is a nonstrictly hyperbolic system. Our analysis in this article is quite fundamental.