一类具有多项式型边界记忆项的非线性热方程解的整体存在与爆破

Global existence and blowup of solutions of the heat equation with a memory boundary of polynomial type

本文研究一类具有多项式型边界记忆项的非线性热方程的解的长时间行为,首先建立比较原理并证明经典解的局部存在性;接下来利用比较原理和Green函数研究解的整体存在和爆破;最后讨论边界爆破并给出爆破速率估计.

This paper deals with the long time behavior of solutions of the heat equation with a memory boundary of polynomial type. We first establish the comparison principle and prove the local existence of classical solutions. Then we study the global existence and blowup of the solutions by using the comparison principle and Green＇s function. At last, we consider the boundary blowup and the blowup rate.