一类具有非线性记忆的退化奇异抛物方程解的爆破

运用上下解方法讨论具有非线性记忆和齐次Dirichlet边界条件的退化奇异抛物方程x~mu_t-(x~ru_x)_x=∫_0u~pds正解的爆破性质,得到方程解在有限时间爆破和全局存在的条件.

Abstract：

This paper deals with the blow-up properties of the solution to the degenerate and singular para-bolic equationx~mu_t-(x~ru_x)_x=∫_0u~pds with non-local memory and homogeneous Dirichlet boundary condi-tions. The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution to exist globally or blow up in finite time are obtained.