We present numerical solutions of a two-dimensional inviscid Burgers equation which
provides an asymptotic description of the Mach reflection of weak shocks. In our
numerical solutions, the incident, reflected, and Mach shocks meet at a triple point,
and there is a supersonic patch behind the triple point, as proposed by Guderley
for steady weak-shock reflection. A theoretical analysis indicates that there is an
expansion fan at the triple point, in addition to the three shocks. The supersonic
patch is extremely small, and this work is the first time it has been resolved.