一类带记忆项的非经典热方程的爆破问题  

BLOW-UP PROBLEM FOR A CLASS OF NON-CLASSICAL HEAT EQUATION WITH MEMORY TERM

作　　者：吴少华[1] 吴迎东 程新 WU Shao-hua;WU Ying-dong;CHENG Xin(Department of Mathematics and Statistics,Wuhan University,Wuhan 430072,China)

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2021年第1期71-78,共8页Journal of Mathematics

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.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.

关 键 词：非经典热方程 记忆边界 爆破 

分 类 号：O175.2[理学—基础数学]