具有多重非线性的非牛顿多方渗流方程的整体存在性与非存在性

Global Existence and Blow-up of Solutions to a Doubly Degenerate Parabolic System with Nonlinear Boundary Conditions

考虑了一个具有多重非线性的抛物模型中,非线性扩散项、非线性反应项和非线性边界流三种非线性机制之间的相互作用.通过构造自相似上解和自相似下解,获得了临界整体存在性曲线和临界Fujita曲线.

This paper deals with interactions among three kinds of nonlinear mechanisms：nonlinear diffusion,nonlinear reaction and nonlinear boundary flux in a parabolic model with multiple nonlinearities.We obtain the critical global existence curve and critical Fujita curve by constructing various self-similar supersolutions and subsolu-tions.