Persistence of wavefronts in delayed nonlocal reaction–diffusion equations
- 作者：Chunhua Ou ; Jianhong Wu
- 关键词：Persistence ; Delay ; Reaction– ; diffusion equations ; Traveling wavefronts ; Nonmonotone nonlinearity ; Delayed induced nonlocality ; Monostable and bistable ; Population dynamics ; Bio-reactor ; Hybrid system ; Hyperbolic– ; parabolic equations
- 刊名：Journal of Differential Equations
- 出版年：2007
- 期刊代码：74_00220396
- 类别：mt
- 出版时间：1 April 2007
- 卷：235
- 期：1
- 页码：219-261
- 文件大小：317 K
摘要
We develop a perturbation argument based on existing results on asymptotic autonomous systems and the Fredholm alternative theory that yields the persistence of traveling wavefronts for reaction–diffusion equations with nonlocal and delayed nonlinearities, when the time lag is relatively small. This persistence result holds when the nonlinearity of the corresponding ordinary reaction–diffusion system is either monostable or bistable. We then illustrate this general result using five different models from population biology, epidemiology and bio-reactors.