【摘要】 在本文中,我们讨论了不满足所谓的拟单调条件的反应扩散方程组的边值问题,定义了在这一般情况下的问题的上下解。再用单调迭代的技巧构造出逼近问题解的单调序列,并证明了在上下解存在的前提下,问题解的存在唯一性。 用这个方法,我们进一步讨论了有关化学中的Belousov-Zhabotinskii反应的Noyes-Field方程组的Dirichlet问题和齐次Neumann问题。得到了前者平衡解的局部稳定的一些充分条件和相应的局部吸引区域,以及后者的“板机效应”。更多还原

【Abstract】 In this paper, we have discussed the boundary-initial problem of the reaction-diffusion systems which do not satisfy the so-called quasi-monotone condition. We have defined the upper-lower solutions of the problem in this general case. Then we use the monotone iteration to contruct a monotone sequence which can approximate the solution of the problem. We have proved that if the upper-lower solutions exist, the problem has a unique solution.Using this method, we have discussed the existence and stability of the Noyes-Field system related to the Belousov-zhabotinskii reaction with the Dirichlet boundary condition and Neumann condition.更多还原