Existence of traveling wavefronts of delayed reaction diffusion systems without monotonicity

By Jianhua Huang, Xingfu Zou. 2003

131 citations recorded by the source corpus.

In this paper, we establish the existence of traveling wavefronts for delayed reaction diffusion systems without quasimonotonicity in the reaction term, by using Schauder's fixed point theorem. We show the merit of our result by applying it to the Belousov-Zhabotinskii reaction model with two delays.

Subfields: Applied Mathematics, Geometry and Topology, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/88cd5033de830641c91d2f14589456a678e59f24

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In Applied Mathematics

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

In Geometry and Topology

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

In Public Health, Environmental and Occupational Health

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

Citations in the corpus

• Traveling Wave Solutions for Delayed Reaction–Diffusion Systems and Applications to Diffusive Lotka–Volterra Competition Models with Distributed Delays (2014, unknown): “Moreover, similar to those in Huang and Zou [12], Li et al. [15, Lemma 3.6] and Ma [18], F : → is completely continuous in the sense of the decay norm | · | σ .”
• Travelling Wave Solutions in Delayed Reaction Diffusion Systems with Partial Monotonicity (2006, methodology): “Addressing (B), Ma([8]), and Huang and Zou([6]) employ the Schauder’s fixed point theorem to relax the requirements for the upper-lower solutions, but with the cost of sacrificing the monotonicity of the iteration sequence.”
• 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.”
• Traveling wave solutions in delayed reaction diffusion systems with applications to multi-species models (2009, methodology): “It is clear that (MQM) and (EMQM) include the monotonicity conditions in [17, 18, 21, 25, 26, 28, 42, 61, 62, 66].”
• Traveling waves for non-local delayed diffusion equations via auxiliary equations☆ (2007, methodology): “When K is such that f (u) is not increasing on [0,K], the monotone iteration method developed in Wu and Zou [12] cannot be used as the involved iteration scheme is no longer monotone.”
• Existence and uniqueness of traveling waves for non-monotone integral equations with applications (2010, background): “[23] J. Wu, X. Zou, Traveling wave fronts of reaction–diffusion systems with delay, J. Dynam.”
• Travelling wave fronts in reaction-diffusion systems with spatio-temporal delays (2006, background): “Recently, many researchers have paid attention to travelling wave solutions for reaction–diffusion equations with time delays, for example, see [1,11,17–19,22,26,29,32, 33,36].”