关键词: 全局存在性, 爆破, Newton渗流方程, 临界曲线

Abstract:

The authors analyzed the large time behavior of solutions to the fast diffusive Newtonian filtration system coupled via the nonlinear boundary sources by the method of constructing various kinds of upper and lower solutions. We got the critical Fujita curve and the critical global existence curve. For many investigated Newtonian filtration equations with nonlinear boundary sources, the critical Fujita curve and the critical global existence curve are usually different. We showed that the critical global existence curve and the critical Fujita curve  are superimposed for Newtonian filtration system coupled via boundary flux.

Key words: global existence, blow up, Newtonian filtration equation, critical curve