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Stability of non-monotone traveling waves for a discrete diffusion equation with monostable convolution type nonlinearity

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Abstract

This paper is concerned with the stability of non-monotone traveling waves for a discrete diffusion equation with monostable convolution type nonlinearity. By using the anti-weighted energy method and nonlin-ear Halanay’s inequality, we prove that all noncritical traveling waves (waves with speeds c > c*, c* is minimal speed) are time-exponentially stable, when the initial perturbations around the waves are small. As a corollary of our stability result, we immediately obtain the uniqueness of the traveling waves.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant No. 11401478). The authors are grateful to the referees for their valuable comments and suggestions which helped them improve the presentation of the paper.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, China

    Zhaoxing Yang & Guobao Zhang

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  1. Zhaoxing Yang
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  2. Guobao Zhang
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Correspondence to Guobao Zhang.

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Yang, Z., Zhang, G. Stability of non-monotone traveling waves for a discrete diffusion equation with monostable convolution type nonlinearity. Sci. China Math. 61, 1789–1806 (2018). https://doi.org/10.1007/s11425-017-9175-2

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  • DOI: https://doi.org/10.1007/s11425-017-9175-2

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