具有Robin边界条件的退化方程的爆破现象

Blow-up Phenomenon of Degenerate Equations with Robin Boundary Condition

考虑了经常被用于模拟湍流过滤现象的退化抛物方程.运用微分不等式,对初始条件进行一些必要限制之后,得到了Robin边界条件下解的爆破时间的下界以及确保解全局存在的条件.最后,证明了齐次Neumann边界条件下解一定在某个有限时刻发生爆破,并得到了爆破时间的上界.

The degenerate parabolic equation,which is often used to simulate turbulent filtration,is considered.By using differential inequality,the lower bound of the blow-up time of the solution under Robin boundary condition and the conditions to ensure the global existence of the solution are obtained.Finally,we prove that the solution must blow-up at a finite time under homogeneous Neumann boundary condition,and obtain the upper bound of blow-up time.