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Traveling Waves in Discrete Periodic Media for Bistable Dynamics

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Abstract

This paper is concerned with the existence, uniqueness, and global stability of traveling waves in discrete periodic media for a system of ordinary differential equations exhibiting bistable dynamics. The main tools used to prove the uniqueness and asymptotic stability of traveling waves are the comparison principle, spectrum analysis, and constructions of super/subsolutions. To prove the existence of traveling waves, the system is converted to an integral equation which is common in the study of monostable dynamics but quite rare in the study of bistable dynamics. The main purpose of this paper is to introduce a general framework for the study of traveling waves in discrete periodic media.

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Xinfu Chen

  2. Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan

    Jong-Shenq Guo

  3. Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan

    Chin-Chin Wu

Authors
  1. Xinfu Chen
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  2. Jong-Shenq Guo
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  3. Chin-Chin Wu
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Correspondence to Jong-Shenq Guo.

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Communicated by D. Kinderlehrer

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Chen, X., Guo, JS. & Wu, CC. Traveling Waves in Discrete Periodic Media for Bistable Dynamics. Arch Rational Mech Anal 189, 189–236 (2008). https://doi.org/10.1007/s00205-007-0103-3

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