非局部反应扩散方程组解的整体存在与爆破

Global existence and blow-up of solution for nonlocal reaction diffusion equations

研究了一类具有非局部源的反应扩散方程组的初边值问题,首先利用上下解方法,构造出不同结构的上解,结合比较原理,得到解的整体存在的充分条件,其次利用特征函数和常微分方程的解,构造问题在有限时刻爆破的下解,得出了解在有限时间内爆破的充分条件.

The initial boundary value problem for a class of reaction diffusion equations with nonloeal source has been studied. First, the different upper solutions have been constructed by the method of up- per and lower solution,and combined with comparison principle,the sufficient conditions for existence of the global solution is obtained. Second, the lower solution which blow-up in finite time＂ has been con- structed by using eigenvalue function and solution of ordinary differential equation. The sufficient-eondi- tions of solution which blow up in finite time have been obtained.