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Shengqiang Zhang, Zhixian Yu, Yanling Meng. STABILITY OF TRAVELING WAVE FRONTS FOR NONLOCAL DIFFUSIVE SYSTEMS[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2063-2081. doi: 10.11948/20230192
Citation: Shengqiang Zhang, Zhixian Yu, Yanling Meng. STABILITY OF TRAVELING WAVE FRONTS FOR NONLOCAL DIFFUSIVE SYSTEMS[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2063-2081. doi: 10.11948/20230192
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STABILITY OF TRAVELING WAVE FRONTS FOR NONLOCAL DIFFUSIVE SYSTEMS

  • 1.

    College of Sciences, Shanghai Institute of Technology, 100 Haiquan Road, Shanghai 201418, China

  • 2.

    Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

    Abstract

  • The paper is concerned with stability of traveling wave fronts for nonlocal diffusive systems. We adopt L1-weighted, L1- and L2-energy estimates for the perturbation systems, and show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave fronts provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev space.

    MSC: 35K57, 35C07, 35R20, 92D25
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