In this paper, we study the blow-up problems for a class of reaction-diffusion system with nonlinear norm-type sources: ut = ∆um+a kup1 vq1 kr1α , vt = ∆vn+b kvp2 wq2 kr2β , wt = ∆wh +c kwp3uq3kr3γ 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.%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 kup1 vq1 kr1α， vt =∆vn+b kvp2 wq2 kr2β， wt =∆wh+c kwp3 uq3 kr3γ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。
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