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.

中文翻译：

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不连续速度的反应扩散方程和几何流的奇异极限

当行波解的速度取决于空间变量并收敛为不连续函数时，我们考虑双稳态反应扩散方程的奇异极限。我们表明解决方案的族收敛到稳定的平衡，以不连续的速度传播。通过应用通过粘度解理论和水平集方程唯一定义的弱几何流动，收敛在时间上是全局的。