Traveling Wave Fronts of Reaction-Diffusion Systems with Delay

By Jianhong Wu, Xingfu Zou. 2001

556 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/79ec35b4b1e90d4179437cd35b12494cf0a4c6ab

How researchers see this paper

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

In Computer Networks and Communications

1. Wan-Tong Li
2. Guo Lin
3. Xingfu Zou
4. Shigui Ruan
5. Zhi-Cheng Wang
6. Ming Ma
7. Jianhua Huang
8. Shiwang Ma

In Modeling and Simulation

1. Wan-Tong Li
2. Guo Lin
3. Xingfu Zou
4. Shigui Ruan
5. Zhi-Cheng Wang
6. Shiwang Ma
7. Jianhong Wu
8. Xiao-Qiang Zhao

In Public Health, Environmental and Occupational Health

1. Wan-Tong Li
2. Guo Lin
3. Shigui Ruan
4. Zhi-Cheng Wang
5. Xingfu Zou
6. Xiao-Qiang Zhao
7. Shiwang Ma
8. Ming Ma

Citations in the corpus

• Existence of traveling wavefronts of delayed reaction diffusion systems without monotonicity (2003, methodology): “As in Ma [5], we will construct a subset in the Banach space C(R,R) equipped with the exponential decay norm, and apply the Schauder’s fixed point theorem to the operator used in Wu and Zou [13] and Ma [5] to establish the existence of a traveling wavefront.”
• Nonmonotone travelling waves in a single species reaction–diffusion equation with delay (2005, background): “This approach (proposed in [28]) works well if 1 < p/δ ≤ e, since in this case the function g is increasing on [0, 1] ⊃ [0, a], thus φ 7→ −δφ(0)+pg(φ(−h)) satisfies the quasimonotonicity condition in [28].”
• Traveling waves for a generalized Holling-Tanner predator-prey model (2017, background): “Though this approach sometimes does not produce results as general as that in [22], it has its own strengths: the upper and lower solutions employed are simple, so the proofs involved are less complex; the approach can be generalized to nonlocal predator–prey systems (such as those with delays [30,3”
• Asymptotic speed of propagation of wave fronts in a lattice delay differential equation with global interaction (2003, background): “…with interaction between patches and the existence of travelling waves can be found in Smith & Thieme (1991), Soet al. (2000, 2001), Wu (1996), Wu & Zou (2001) and references therein, while discussions on asymptotic speed can be found in Aronson (1977), Aronson & Weinberger (1975, 1978),…”
• Existence, Uniqueness, and Stability of Generalized Traveling Waves in Time Dependent Monostable Equations (2011, background): “... reaction diffusion equations of KPP type; see [5–7,14,21,27,29,32,36,37,40,44,67], and references therein for space and/or time periodic reaction diffusion equations of KPP type; see [14,18, 33,38,39,63,64],andreferencesthereinforKPPmodelsinrandommedia;see[28,30,59,60], andreferencesthereinforti”
• Traveling wave fronts for generalized Fisher equations with spatio-temporal delays (2007, unknown): “See [1,3,4,9,12–14,16,19,21,23–27] and the references therein.”
• Uniqueness of travelling waves for nonlocal monostable equations (2004, unknown): “, [1], [4], [6], [13], [11], [14], [5].”
• Existence of travelling wave solutions in delayed reaction–diffusion systems with applications to diffusion–competition systems (2006, methodology): “Wu and Zou [33] further considered more general reaction–diffusion systems with a single delay of the form”
• Traveling Wave Solutions for Delayed Reaction–Diffusion Systems and Applications to Diffusive Lotka–Volterra Competition Models with Distributed Delays (2014, methodology): “To obtain the existence of traveling wave solutions of delayed systems, Wu and Zou [38] used a monotone iteration scheme if a delayed system is cooperative in the sense of proper ordering, see also Ma [18].”