中文摘要：

考虑描述核反应动力学模型的非局部反应扩散方程自由边界问题,通过拉直边界并利用压缩映射原理给出解的存在性与唯一性,并运用Hopf引理证明了自由边界的单调性.

英文摘要：

A nonlocal reaction-diffusion equation with free boundary arising in nuclear reactor dynamics is considered.The existence and uniqueness of the solution is carried out by making a change of variables to flatten the free boundary and using contraction mapping principle.The monotonic behavior of the free boundary is obtained by applying Hopf lemma.