一类具有记忆边界条件的抛物型方程组解的性质

Properties of a Parabolic System with Memory boundary Condition

摘要:

研究一类带非线性记忆项边界条件的抛物型方程组的爆破性质，通过构造方程组的上、下解及积分估计等技巧，得到方程组的解整体存在和有限时刻爆破的完整分类；同时，在某些条件下讨论了爆破点的分布.

Abstract:

We study the blow-up for a parabolic system with a nonlinear memory boundary condition. By using the super-sub solution method and the integration technique, we obtain the complete classification for finite time blow-up and global existence. At the same time, we consider the localization of blow-up set under certain conditions.