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

Singular limits of reaction diffusion equations and geometric flows with discontinuous velocity