A FREE-BOUNDARY PROBLEM FOR ONE-DIMENSIONAL EQUATIONS OF A VISCOUS-GAS

Utilizing the unique solution (w(s),z(s)) to the singular nonlinear two-point boundary value problem (1.11), the authors construct a unique self-similar solution (phi(t),v(x,t),u(x,t)) = (Yt,v(x/t),u(x/t)) to the free boundary problem (1.1)-(1.6), in which (1.1) and (1.2) are one-dimensional equations of a viscous gas. The arguments are elementary which involve only the use of the shooting method and the integral representations for (w(s),z(s)).