带奇异项的拟线性抛物方程组在第二类边界条件下解的猝灭

摘要

In this paper,we considered a class of initial boundary value problem of degenerate quasilinear parabolic system containing singular term under the second boundary conditions.We obtained the existence of solutions through the upper and lower solutions and used the solution of the boundary problem of elliptic equation to construct a lower solutions of initial boundary value problem.Thus we proved that solutions of parabolic system would quench in finite time under certain condition.%为探讨一类含有奇异项的退缩拟线性抛物型方程组在第二类边界条件下的初边值问题,通过上、下解方法得到了解的存在性,并利用椭圆型方程边值问题的解构造初边值问题的一对下解,由此证明了在一定条件下问题的解会在有限时刻发生猝灭.