Periodic Traveling Waves for Diffusion Equations with Time Delayed and Non-local Responding Reaction
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- 作者：Dawn Duehring and Wenzhang Huang
- 关键词：Reaction ; diffusion equations ; time delay and non ; local response ; Periodic traveling waves ; singular perturbation ; integral equations
- 刊名：Journal of Dynamics and Differential Equations
- 出版时间：June, 2007
- 出版年：2007
- 期刊代码：31_10407294
- 类别：mt
- 卷：19
- 期：2
- 页码：457-477
- 数据来源：sp
摘要
We develop a singular perturbation technique to study the existence of periodic traveling wave solutions with large wave speed for a class of reaction-diffusion equations with time delay and non-local response. Unlike the classical singular perturbation method, our approach is based on a transformation of the differential equations to integral equations in a Banach space that reduces the singular perturbation problem to a regular perturbation problem. The periodic traveling wave solutions then are obtained by the use of Liapunov-Schmidt method and a generalized implicit function theorem. The general result obtained has been applied to a non-local reaction-diffusion equation derived from an age-structured population model with a logistic type of birth function.