A generalized one phase Stefan problem as a vanishing viscosity limit

We study the vanishing viscosity limit of a nonlinear diffusion equation describing chemical reaction interface or the spatial segregation interface of competing species, where the diffusion rate for the negative part of the solution converges to zero. As in the standard one phase Stefan problem, we prove that the positive part of the solution converges uniformly to the solution of a generalized one phase Stefan problem. This information is then employed to determine the limiting equation for the negative part, which is an ordinary differential equation.