Abstract
In this paper, we investigate a cooperative system with nonlocal dispersals. It is well known that the existence of traveling wave fronts is established by Li and Lin (Appl Math Comput 204:738–744, 2008). We prove that the traveling wave fronts with the relatively large wave speed are exponentially stable as perturbation in some exponentially weighted spaces, when the difference between initial data and traveling wave fronts decays exponentially at negative infinity, 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.
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This author was supported by Natural Science Foundation of Shanghai (no.18ZR1426500).
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Yu, Z., Pei, J. Stability of traveling wave fronts for a cooperative system with nonlocal dispersals. Japan J. Indust. Appl. Math. 35, 817–834 (2018). https://doi.org/10.1007/s13160-018-0313-0
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DOI: https://doi.org/10.1007/s13160-018-0313-0