Entire solutions in monostable reaction-diffusion equations with delayed nonlinearity

By Wan-Tong Li, Zhi-Cheng Wang, Jianhong Wu. 2008

93 citations recorded by the source corpus.

Abstract Entire solutions for monostable reaction–diffusion equations with nonlocal delay in one-dimensional spatial domain are considered. A comparison argument is employed to prove the existence of entire solutions which behave as two traveling wave solutions coming from both directions. Some new entire solutions are also constructed by mixing traveling wave solutions with heteroclinic orbits of the spatially averaged ordinary differential equations, and the existence of such a heteroclinic orbit is established using the monotone dynamical systems theory. Key techniques include the characterization of the asymptotic behaviors of solutions as t → − ∞ in term of appropriate subsolutions and supersolutions. Two models of reaction–diffusion equations with nonlocal delay arising from mathematical biology are given to illustrate main results.

Subfields: Applied Mathematics, Control and Systems Engineering, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/3bc94469593a66ecfb5cdfc7539d2bb9284acb7f

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In Applied Mathematics

1. Ming Mei
2. Chi-Tien Lin

In Control and Systems Engineering

1. Chi-Kun Lin
2. Ming Mei
3. Chi-Tien Lin
4. Joseph W.-H. So

In Public Health, Environmental and Occupational Health

1. Chi-Kun Lin
2. Ming Mei
3. Chi-Tien Lin
4. Joseph W.-H. So
5. Xingfu Zou

Citations in the corpus

• Traveling wavefronts for time-delayed reaction-diffusion equation: (II) Nonlocal nonlinearity (2009, background): “For other interesting research works related to this topic, please refer to [1–34] and the references therein.”