一类具扩散和时滞Belousov-Zhabotinskii系统的行波解

The Traveling Solutions to a Belousov-Zhabotinskii System with Delay and Diffusion

研究一般的带时滞的反应扩散方程组的行波解,这儿反应项具混拟单调性质,我们定义了相应的行波解的耦合上下解,以耦合上下解为初始迭代函数构造了耦合迭代序列,并且证明了在一定的单调性条件下该耦合序列收敛于行波解.以一个具体的带时滞的Belousov-Zhabotinskii模型为例,建立了有序的拟上解和拟下解并且得到行波解的存在性.

This paper deals with the traveling solutions of the general delayed reaction difl＇usion system, where the reaction function possesses a mixed quasimonotone property. The definition of the coupled upper and lower solutions of the corresponding traveling wave equation were given. By the technique of coupled iteration where the initial data is a pair of coupled upper and lower solutions, the monotonicity property is ensured such that the sequence converges to the traveling wave solution. The main result is illustrated by and applied to a delayed Belousov- Zhabotinskii model with delay for which the required pair of ordered quasi-upper and quasi-lower solutions are constructed and then the existence of a traveling wavefront is obtained.