The paper deals with blow-up phenomena for the following coupled reaction-diffusion system with nonlocal boundary conditions:$\{\begin{array}{ccc}& u_t=\nabla ·\left({\rho }_1\left(u\right)\nabla u\right)+a_1\left(x\right)f_1\left(v\right),\hfill & (x,t)\in D\times (0,T),\hfill \\ & v_t=\nabla ·\left({\rho }_2\left(v\right)\nabla v\right)+a_2\left(x\right)f_2\left(u\right),\hfill & (x,t)\in D\times (0,T),\hfill \\ & \frac{\partial u}{\partial \nu }=k_1\left(t\right){\int }_D{g}_1\left(u\right)\mathrm{d}x,\frac{\partial v}{\partial \nu }=k_2\left(t\right){\int }_D{g}_2\left(v\right)\mathrm{d}x,\hfill & (x,t)\in \partial D\times (0,T),\hfill \\ & u(x,0)=u_0\left(x\right),v(x,0)=v_0\left(x\right),\hfill & x\in \overline{D}.\hfill \end{array}$Based on some differential inequalities and Sobolev inequality, we establish conditions on the data to guarantee the occurrence of the blow-up. Moreover, when the blow-up occurs, explicit lower and upper bounds on blow-up time are obtained. At last, an example is presented to illustrate our main results.

本文讨论了以下具有非局部边界条件的耦合反应扩散系统的爆破现象：$\{\begin{array}{ccc}& {你}_{吨}=\nabla ·\left({\rho }_1\left(你\right)\nabla 你\right)+{\mathrm{一种}}_1\left(X\right)F_1\left(v\right),\hfill & (X,吨)\in D\times (0,吨),\hfill \\ & v_{吨}=\nabla ·\left({\rho }_2\left(v\right)\nabla v\right)+{\mathrm{一种}}_2\left(X\right)F_2\left(你\right),\hfill & (X,吨)\in D\times (0,吨),\hfill \\ & \frac{\partial 你}{\partial \nu }={克}_1\left(吨\right){\int }_D{G}_1\left(你\right)\mathrm{d}X,\frac{\partial v}{\partial \nu }={克}_2\left(吨\right){\int }_D{G}_2\left(v\right)\mathrm{d}X,\hfill & (X,吨)\in \partial D\times (0,吨),\hfill \\ & 你(X,0)={你}_0\left(X\right),v(X,0)=v_0\left(X\right),\hfill & X\in \overline{D}.\hfill \end{array}$基于一些微分不等式和Sobolev不等式，我们在数据上建立条件以保证爆炸的发生。此外，当发生爆破时，可以获得爆破时间的明确下限和上限。最后，给出了一个例子来说明我们的主要结果。