具有非线性范数型源的反应扩散方程组解的爆破性质
BLOW-UP PROPERTIES FOR A REACTION-DIFIUSION SYSTEM WITH NONLINEAR NORM-TYPE SOURCES

本文研究了一类带有非线性范数型源的反应扩散方程组ut=△um+a||up1vq1||αr1，vt=△vn+b||vp2wq2||βr2，wt=△wh+c||wp3uq3||γr3在齐次Dirichlet边界条件下解的爆破问题.利用上下解方法和构造辅助函数的技巧，得到了方程组解的整体存在与爆破的准则，将当前的一些研究结果推广到更复杂的情形.
In this paper, we study the blow-up problems for a class of reaction-difiusion system with nonlinear norm-type sources:ut=△um+a||up1vq1||αr1,vt=△vn+b||vp2wq2||βr2,wt=△wh+c||wp3uq3||γr3 subject to homogeneous Dirichlet conditions. By using upper-lower solution method and constructing auxiliary functions' techniques, we obtain the criteria for global existence or finite time blow-up, which extend some results of the current research to more complex situations