中文摘要：

本文研究了一类描述可燃混合气体的热传播过程理论的退化抛物型方程组.借助于椭圆问题的特征值与特征函数理论,通过构造不同的上、下解得到了方程组解的整体存在与有限时刻爆破的条件.此结果不仅扩充了只讨论两个函数的半线性问题,并且证明了方程组中的系数ai,边界条件中的权重函数gi（x,y）以及指数li在决定问题解的爆破与否中起着关键的作用.

英文摘要：

This paper studies a class of degenerate parabolic equations coupled via nonlinear sources and with nonlocal boundary conditions. These equations can be used to describe the thermoelasticity theory such as heat propagation of the combustible mixture gases. This study is thus meaningful in various branches of applied mathematics. With the help of the theory of eigenvalue and eigenfunction, we obtained the blow-up and global existence conditions of the solutions by constructing various super- solutions and subsolutions. These results not only extend the semi-linear problems which only dealed with two functions, but also show that the coefficient ai, the weight function gi（x, y） and the exponent li play substantial roles in determining whether the solutions are global or blow-up.