关键词: 牛顿渗流方程, 可变源, 爆破, 下界, 有效性

Abstract:

In this paper, we consider the blow-up phenomenon to a type of Newtonian filtration equation with variable source subject to homogeneous Neumann boundary condition. We give two methods to determine the lower bound for blow-up time of solution in $\Omega \in {{\mathbb{R}}^{3}}$ if the solutions blow up by energy estimation method and diferential inequality technique. Moreover, the effectiveness of these methods are also discussed.

Key words: Newtonian filtration equation, Variable source, Blow-up, Lower bound, Effectiveness