Persistence of wavefronts in delayed nonlocal reaction-diffusion equations

By Chunhua Ou, Jianhong Wu. 2007

137 citations recorded by the source corpus.

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.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/176e33148b0d5dd77bbe675652ade661d57c4300

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Genetics

1. Wan-Tong Li
2. Guo Lin
3. Zhi-Cheng Wang
4. Jian Fang
5. Shigui Ruan
6. Xiao-Qiang Zhao
7. Junjie Wei
8. Ming Ma

In Modeling and Simulation

1. Wan-Tong Li
2. Guo Lin
3. Zhi-Cheng Wang
4. Jian Fang
5. Junjie Wei
6. Xiao-Qiang Zhao
7. Shigui Ruan
8. Ming Ma

In Public Health, Environmental and Occupational Health

1. Wan-Tong Li
2. Guo Lin
3. Zhi-Cheng Wang
4. Shigui Ruan
5. Jian Fang
6. Xiao-Qiang Zhao
7. Junjie Wei
8. Ming Ma

Citations in the corpus

• Bistable wavefronts in a diffusive and competitive Lotka-Volterra type system with nonlocal delays (2008, background): “In particular, we should mention the recent result of Ou and Wu [42], in which they considered the persistence of wavefronts for both monostable and bistable systems with nonlocal delay.”
• Traveling Wave Solutions for Delayed Reaction–Diffusion Systems and Applications to Diffusive Lotka–Volterra Competition Models with Distributed Delays (2014, unknown): “[17], Ma [18,19], Ma and Wu [20], Mei [22], Ou and Wu [23], Schaaf [26], Smith and Zhao [29], Thieme and Zhao [31], Wang [33], Wang et al.”
• Existence and uniqueness of traveling waves for non-monotone integral equations with applications (2010, background): “Ou and Wu [17] established the persistence of wavefronts for time-delayed nonlocal reaction–diffusion equations via the perturbation method.”
• Traveling Fronts in Monostable Equations with Nonlocal Delayed Effects (2008, background): “[16], Ou and Wu [34] showed the persistence of traveling wave solutions for reaction–diffusions with nonlocal and delayed nonlinearities when the time lag is relatively small, which can be applied to not only the monostable case but also the bistable case.”
• Traveling wave solutions in delayed reaction diffusion systems with applications to multi-species models (2009, methodology): “For scalar equations with diffusion and delays, the existence of traveling wave solutions has been widely studied by using the comparison principle [29, 30, 31, 42, 46, 47, 51, 55, 57, 65] and perturbation method [3, 6, 7, 34].”
• Spreading speeds and travelling waves for non-monotone time-delayed lattice equations (2010, background): “Recently, there have been increasing efforts on the existence of travelling waves for non-monotone delayed evolution equations (Wu & Zou 2001; Faria & Trofimchuk 2006; Faria et al. 2006; Ou & Wu 2007), in which these authors showed the existence for sufficiently large wave speeds or small delays.”