In this paper, we establish the Fujita type theorem for a homogeneous Neumann outer problem of the coupled quasilinear convection–diffusion equations and formulate the critical Fujita exponent. Besides, the influence of diffusion term, reaction term, and convection term on the global existence and the blow-up property of the problem is revealed. Finally, we discuss the large time behavior of the solution to the outer problem in the critical case and describe the asymptotic behavior of the solution.

中文翻译：

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一类耦合拟线性对流扩散方程的Fujita型定理

在本文中，我们为拟线性对流扩散方程的齐次Neumann外部问题建立了Fujita型定理，并提出了临界的Fujita指数。此外，还揭示了扩散项，反应项和对流项对整体存在性和问题的爆炸性质的影响。最后，我们讨论了关键情况下外部问题解的长时间行为，并描述了该解的渐近行为。