一类耦合退化抛物方程组解的整体存在与爆破

Global Existence and Blow-up of Solutions for a Coupled Degenerate Parabolic System

研究一类通过边界条件耦合的非线性快扩散方程组解的长时间行为,如解关于时间的整体存在性以及解在有限时刻发生爆破等性质.利用上、下解方法得到了可以用来刻画解是否整体存在的临界指标,即整体存在临界曲线.

We studied the large time behavior of a class of nonlinear diffusion equations coupled by the boundary conditions, such as global existence in time and blowing up in a finite time. By the upper and lower solutions method, we obtained the critical global existence curve which can be used to describe whether the solution is global existence.