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| 摘要: |
| 本文考虑了一类带记忆项的非经典热方程，证明解会在有限时间爆破，而且爆破只会发生在边界.主要结论是:首先利用Green函数与Banach压缩映射定理，建立了问题的经典解；其次，利用经典解，证明了解是有限时间爆破的；最后，证明了一个关于非经典热方程解的性质，利用这个性质，证明了解是在边界上爆破的. |
| 关键词: 非经典热方程 记忆边界 爆破 |
| DOI： |
| 分类号:O175.2 |
| 基金项目: |
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| BLOW-UP PROBLEM FOR A CLASS OF NON-CLASSICAL HEAT EQUATION WITH MEMORY TERM |
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WU Shao-hua,WU Ying-dong,CHENG Xin
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| Abstract: |
| In this article, we consider a non-classical heat equation with a memory boundary condition. We have proved that our solutions blow-up in the finite time, and blow-up only occur on the boundary. Firstly, we construct the classical solution by using the Green function and Banach fixed point theorem.And then we prove the solution blow-up in the finite time. Lastly, we prove the solution only occur on the boundary by using the theorem 2.1. |
| Key words: non-classical heat equation memory boundary condition blow-up |
