Travelling wave fronts in reaction-diffusion systems with spatio-temporal delays |
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Authors: | Zhi-Cheng Wang Wan-Tong Li Shigui Ruan |
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Affiliation: | a School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China b Department of Mathematics, Hexi University, Zhangye, Gansu 734000, People's Republic of China c Department of Mathematics, University of Miami, P.O. Box 249085, Coral Gables, FL 33124-4250, USA |
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Abstract: | This paper deals with the existence of travelling wave fronts in reaction-diffusion systems with spatio-temporal delays. Our approach is to use monotone iterations and a nonstandard ordering for the set of profiles of the corresponding wave system. New iterative techniques are established for a class of integral operators when the reaction term satisfies different monotonicity conditions. Following this, the existence of travelling wave fronts for reaction-diffusion systems with spatio-temporal delays is established. Finally, we apply the main results to a single-species diffusive model with spatio-temporal delay and obtain some existence criteria of travelling wave fronts by choosing different kernels. |
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Keywords: | 35K57 34K10 35B20 |
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