Existence and uniqueness of traveling waves for non-monotone integral equations with applications

By Jian Fang, Xiao-Qiang Zhao. 2010

121 citations recorded by the source corpus.

Abstract A class of integral equations without monotonicity is investigated. It is shown that there is a spreading speed c ∗ > 0 for such an integral equation, and that its limiting integral equation admits a unique traveling wave (up to translation) with speed c ⩾ c ∗ and no traveling wave with c c ∗ . These results are also applied to some nonlocal reaction–diffusion population models.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/fe4fc4a3d1e18345ca34000251783d4315927b32

How researchers see this paper

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

In Applied Mathematics

1. Arnaud Ducrot
2. Ming Mei
3. Xiongfeng Yang

In Modeling and Simulation

1. Qifeng Zhang
2. Arnaud Ducrot
3. Ming Mei

In Public Health, Environmental and Occupational Health

1. I-Liang Chern
2. Qifeng Zhang
3. Xiongfeng Yang
4. Arnaud Ducrot
5. Ming Mei
6. Chi-Kun Lin

Citations in the corpus

• Spatial propagation for a two component reaction–diffusion system arising in population dynamics (2016, result): “However let us mention the works of Theime [27], Thieme and Zhao [29] and Fang and Zhao [13] (see also the references cited therein) for the study of the asymptotic speed of spread for integral equations, Fang et al [12] for delay lattice equations and Hsu and Zhao [17], Wang and Castillo-Chavez [32”
• Stability of non-monotone critical traveling waves for reaction-diffusion equations with time-delay (2015, background): “For details, we refer to [3,5,7,14,32,33], see also the summary in [13].”