Traveling wavefronts in a bistable reaction diffusion system with spatio-temporal delay

✍ Scribed by Hai-Qin Zhao

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 256 KB
• Volume: 16
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2011.02.017

✦ Synopsis

This paper is concerned with a reaction-diffusion system with spatio-temporal delay. Under the bistable assumptions, the existence of traveling wavefronts is established by transforming the system with spatio-temporal delay to a three-dimensional reactiondiffusion system without delay. The uniqueness (up to a translation) of the traveling wavefronts is also proved by using upper and lower solutions technique. From the point of view of epidemiology, the result implies that the spatio-temporal delay appeared in the interaction term is not sensitive to the moving zone for the transition from the disease-free state to the infective state.