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Abstract

We consider the nonlocal analogue of the Fisher-KPP equation where $ \mu$ is a Borel-measure on $ \mathbb{R}$ with $ \mu(\mathbb{R})=1$ and $f$ satisfies $f(0)=f(1)=$ $0$ and $f >0$ in $(0,1)$ . We do not assume that $ \mu$ is absolutely continuous. The equation may have a standing wave solution (a traveling wave solution with speed $0$ ) whose profile is a monotone but discontinuous function. We show that there is a constant $c _{*}$ such that it has a traveling wave solution with monotone profile and speed $c$ when $c \geq c_{*}$ while no periodic traveling wave solution with average speed $c$ when $c

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我们考虑Fisher-KPP方程的非局部类似，其中$ \mu$是$ \mathbb{R}$上的borel测度，$ \mu(\mathbb{R})=1$和$f$在$(0,1)$中满足$f(0)=f(1)=$$0$和$f >0$。我们不假设$ \mu$是绝对连续的。方程可能有一个驻波解(速度为$0$的行波解)，其剖面是一个单调但不连续的函数。我们证明了存在一个常数$c _{*}$，使得它在$c \geq c_{*}$时具有单调剖面和速度$c$的行波解，而在$c

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