ShaoZhong Chen
lt is proved by stochastic analysis method that if u0 is bounded and mea- surable and f> 0 then the solution of Cauchy problem of the quasilinear parabolic partial differential equation u0+f(u)ux+=0 , u(0,x) =u0 (x) xonverges to the entropy solution of the quasilinear partial differential equation u0 +f (u)ux=0 , u(0,x) = u0(x), as - 0, that is the validity of " vanishing viscosity" method for the equation. This is the well known result due to Oleinik by using difference method in 1975. The result of this paper suggests the importance of probabilistic method for solving nonlinear partial differeatial equations.