一类退化的抛物型方程组弱解的整体存在性和爆破

Large Global Existence and Blow-Up of Weak Solutions to a Degenerate Parabolic System

考虑了一个带有齐次Dirichlet边界条件的抛物型方程组,这类方程组描述了具有非线性传导的混合物在热传导或燃烧过程中的扩散问题,函数u,v分别表示参加这一反应扩散过程中可燃物的温度.给出在临界状态下弱解整体存在性和有限时刻爆破的条件,主要借助于比较原理,通过构造整体存在的上解和分片光滑的下解得到.

This paper deals with a degenerate parabolic system with homogeneous Dirichlet boundary conditions. The coupled equations can be used to describe diffusion processes of heat and burning in mixed media with nonlinear conductivity and volume release, and the functions u and v here can be treated as temperatures of interacting components in the combustible. This short paper gives the conditions on global existence and blow-up of weak solutions in the critical state. The result is concluded by constructing the super-solution for globe existence and sub-solution for blow-up, and using the weak comparison principal.