中文摘要：

该文证明了非柱形区域中抛物方程解的两个唯一性．一个是边界随时间变化的区域中解的唯一延拓性，另一个是边界随时间变化的外区域中解的倒向唯一性．

英文摘要：

This work concerns the uniqueness of solutions to parabolic equations in domains which are moving in time. Two uniqueness results are proved. The first one is the unique continuation property for parabolic equations in non-cylindrical domains. The second one is the backward uniqueness for parabolic equations in exterior domains with moving boundary.