一类非线性多孔介质方程解的爆破问题

Some questions of blow-up of solution to a nonlinear porous medium equation

在任意光滑的有界区域ΩR^n(n≥3)内研究了一类非线性的多孔介质方程解的爆破问题。借助于合适的辅助函数,不仅给出了方程的解是否爆破的条件,而且当解发生爆破时,也给出了爆破时间的上界与下界估计。

Some questions of blow-up for a type of nonlinear porous medium equation in any smooth bounded domain Ω C Rn （ n ≥ 3 ） are discussed. By means of suitable defined auxiliary functions, the conditions which ensure that the blow-up occurs or does not occur are given, but also the lower bound and upper bound for the time of blow-up are determined if blow-up occurs.