Asymptotic behaviour of supersonic flow past a convex combined wedge

The supersonic flow past a convex combined wedge is discussed. Here the surface of the wedge is composed of two straight lines connected by a convex smooth curve. Under the assumptions that the shock is weak, the vertex of the wedge is less than a critical value and the difference of the slope of these two lines is small, the author proves the global existence of solution with shock front and obtains the asymptotic behaviour of the solution.