  We consider the singular limit of a bistable reaction diffusion equation in
the case when the velocity of the traveling wave solution depends on the space
variable and converges to a discontinuous function. We show that the family of
solutions converges to the stable equilibria off a front propagating with a
discontinuous velocity. The convergence is global in time by applying the weak
geometric flow uniquely defined through the theory of viscosity solutions and
the level-set equation.
