Abstract: In this paper we have obtained the existence of weak solutions of the small disturbance equations of steady two-dimension flow
v_t-u_x=0 u_t-(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.