In this paper, the blow-up solutions of the following reaction-diffusion systems are studied:$\{\begin{array}{c}{(h(u))}_t=\mathrm{\nabla }\cdot (b(u)\mathrm{\nabla }u)+f(x,u,v,t),\hfill \\ {(k(v))}_t=\mathrm{\nabla }\cdot (d(v)\mathrm{\nabla }v)+g(x,u,v,t),\hfill & (x,t)\in D\times (0,T),\hfill \\ \frac{\partial u}{\partial n}=0,\frac{\partial v}{\partial n}=0,\hfill & (x,t)\in \partial D\times (0,T),\hfill \\ u(x,0)=u_0(x),v(x,0)=v_0(x),\hfill & x\in \bar{D},\hfill \end{array}$ where $D\subset {\mathbb{R}}^n(n\ge 2)$ is a bounded region and the boundary ∂D of D is smooth. Sufficient conditions to ensure the existence of the blow-up solution of this problem are obtained. For the blow-up solution, we also get an upper bound on the blow-up time and an upper estimate of the blow-up rate. Our research mainly relies on the use of the maximum principles of weakly coupled parabolic systems and the first-order differential inequality technique.

本文研究了以下反应扩散系统的爆炸解决方案：$\{\begin{array}{c}{（H（ü））}_{Ť}=\mathrm{\nabla }\cdot （b（ü）\mathrm{\nabla }ü）+F（X，ü，v，Ť），\hfill \\ {（ķ（v））}_{Ť}=\mathrm{\nabla }\cdot （d（v）\mathrm{\nabla }v）+G（X，ü，v，Ť），\hfill & （X，Ť）\in d\times （0，Ť），\hfill \\ \frac{\partial ü}{\partial ñ}=0，\frac{\partial v}{\partial ñ}=0，\hfill & （X，Ť）\in \partial d\times （0，Ť），\hfill \\ ü（X，0）={ü}_0（X），v（X，0）=v_0（X），\hfill & X\in \stackrel{〜}{d}，\hfill \end{array}$ 在哪里 $d\subset {\mathbb{[R}}^{ñ}（ñ\ge \mathrm{2个}）$是有界区域和所述边界∂ d的d是光滑的。获得了足够的条件以确保存在该问题的爆炸解决方案。对于爆破解决方案，我们还获得了爆破时间的上限和爆破率的上限估计。我们的研究主要依靠弱耦合抛物线系统的最大原理和一阶微分不等式技术的使用。