中文摘要：

研究了带有Neumann边界条件和非局部源项的非局部扩散方程的爆破问题.在非负,非平凡且有界的初值条件下,利用微分理论,得到了非负,非平凡解将在有限时间内爆破,同时给出了解的爆破时间和爆破率。

英文摘要：

The solutions blow-up in finite time is an important feature of many diffusion equations. This paper stud- ied the blow-up for a non-local diffusion problem with Neumann boundary conditions and a non-local source term. In the condition of the non-negative, non-trivial and bounded initial datum, we obtained that the non-negative and non-trivial solutions would blow up in finite time and got the blow-up time and the blow-up rate.