一类反应扩散方程组解的爆破  

Blow-up for a reaction-diffusion equations

作　　者：容跃堂[1] 崔美英[1] 

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《纺织高校基础科学学报》2011年第4期495-498,共4页Basic Sciences Journal of Textile Universities

摘　　要：研究了一类带有非局部源的反应扩散方程组解的爆破性质和同时爆破.首先运用上下解方法,利用拉普拉斯算子的特征值和特征函数以及常微分方程的解,构造问题的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,其次利用反证法,得出了解同时爆破的充分条件.The blow-up and simultaneous blow-up properties of solutions for a reaction-diffusion equations with nonlocal sources have been studied in this paper.The sufficient conditions for blow-up of the solutions in finite time are proved by the method of upper and lower solutions.The lower solutions blow-up in finite time have been constructed by using eigenvalue and eigenfuction of Laplacian and solution of an ordinary differential equation.The sufficient conditions of the simultaneous blow-up are also obtained by proof by contradiction.

关 键 词：非局部源 反应扩散方程组 爆破 同时爆破 

分 类 号：O175.29[理学—数学]