In this paper, we mainly consider a class of free boundary problems of reaction-diffusion equations with nonlocal diffusion coefficient. By the well-known contraction mapping theorem, the uniqueness and existence of solutions are established for the local time $t>0$. Secondly, we give some sufficient conditions for vanishing phenomenon and spreading phenomenon, respectively. Further, we prove a spreading-vanishing dichotomy for this model. Finally, we obtain the asymptotic spreading speed when spreading happens.

中文翻译：

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具有非局部扩散系数和自由边界的对数方程的扩展与消失

在本文中，我们主要考虑一类具有非局部扩散系数的反应扩散方程的自由边界问题。通过众所周知的收缩映射定理，可以确定局部时间解的唯一性和存在性$Ť>0$。其次，我们分别给出了消失现象和扩散现象的充分条件。此外，我们证明了该模型的扩散消失二分法。最后，我们获得了发生扩展时的渐近扩展速度。