Stability of invasion traveling waves for a competition system with nonlocal dispersals

Abstract

In this paper, we mainly investigate the stability of invasion traveling waves for a competition system with nonlocal dispersals. We prove that the invasion traveling waves are exponentially stable as perturbation in some exponentially weighted spaces, when the difference between initial data and traveling waves decays exponentially as , but in other locations, the initial data can be very large. The adopted method is to use the weighted energy and the squeezing technique with some new flavors to handle the nonlocal dispersals.

Keywords:

• Stability
• competitive system
• nonlocal dispersal
• comparison principle
• weighted energy

AMS Subject Classifications:

• 35C07
• 92D25
• 35B35

Acknowledgements

Z.X. Yu would like to thank Memorial University of Newfoundland for its kind hospitality during his visit there. We are very grateful to the referees and the editors for their helpful suggestions which have led to an improvement of our original manuscript.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of Z.X. Yu was partially supported by National Natural Science Foundation of China, by Shanghai Leading Academic Discipline Project [No. XTKX2012], by Innovation Program of Shanghai Municipal Education Commission [No. 14YZ096] and by the Hujiang Foundation of China (B14005). The research of W.G. Zhang was partially supported by National Natural Science Foundation of China [No. 11471215], by Shanghai Leading Academic Discipline Project [No. XTKX2012] and by the Hujiang Foundation of China (B14005).