Traveling Wavefronts for Delayed Reaction-Diffusion Systems via a Fixed Point Theorem

By Shiwang Ma. 2001

345 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Genetics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/242b436153b0e3407ab73a039ec09f01c523b7ed

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. Shigui Ruan
4. Xingfu Zou
5. Zhi-Cheng Wang
6. Ming Ma
7. Jianhua Huang
8. Haiyan Wang

In Genetics

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

In Public Health, Environmental and Occupational Health

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

Citations in the corpus

• Traveling wave solutions in delayed reaction diffusion systems with applications to multi-species models (2009, methodology): “φ 1 (t) ≤ F1(φ1, φ2, · · · , φn)(t), F1 ( φ1, φ2, · · · , φn ) (t) ≤ φ1(t) (14) for all φj(t) ∈ {φj(t), φj(t)}, t ∈ R and j ∈ I1, for which one refers to [21, 28, 61].”
• Traveling waves of diffusive predator-prey systems: Disease outbreak propagation (2012, background): “[17, 37, 40, 57]), where suitable invariant sets are carefully constructed and the order-preserving properties of the involved operators are proved.”
• Monotone traveling wavefronts of the KPP-Fisher delayed equation (2010, background): “The above mentioned works [23] show that continuous and piece-wise C1−continuous lower (upper) solutions φ± still can be used if some sign conditions are fulfilled at the points of discontinuity of φ±.”
• Traveling wave solutions for a continuous and discrete diffusive predator–prey model (2017, background): “For this aspect, we refer the reader to the works [23, 17, 18, 21, 15, 19, 22] for the continuous case and [16, 20] for the discrete case.”
• On the existence of traveling waves for delayed reaction–diffusion equations☆ (2009, methodology): “Wu and Zou [19], Ma [10,11], and Wang, Li and Ruan [17] and others obtained the existence of traveling wave solutions by constructing lower solutions and upper solutions of the associated ordinary differential equation and applying monotone iteration techniques or fixed point theorems.”
• Erratum to “Traveling Wave Fronts of Reaction-Diffusion Systems with Delays” [J. Dynam. Diff. Eq. 13, 651, 687 (2001)] (2008, methodology): “The validity of these theorems can be verified by the smoothening procedure used in [2].”
• Traveling wavefronts in diffusive and cooperative Lotka–Volterra system with delays (2002, methodology): “Note that this technique has also been recently used by So and Zou [10] to the diffusive Nicholson’s blowflies equation with delay, and by Wu and Zou [13] and Ma [7] to the Belousov–Zhabotinskii reaction model with delay.”
• Travelling Wave Solutions in Delayed Reaction Diffusion Systems with Partial Monotonicity (2006, methodology): “, Pao([10]) or Ye and Li([18]) and the references therein), and the Schauder’s fixed point theorem technique employed in Ma([8]), and Huang and Zou([6]).”
• 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.”
• 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].”