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Mathematische Annalen

, Volume 326, Issue 1, pp 123–146 | Cite as

Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics

  • Xinfu Chen
  • Jong-Shenq Guo

Abstract.

 We study traveling waves of a discrete system
$$$$
where f and g are Lipschitz continuous with g increasing and f monostable, i.e., f(0)=f(1)=0 and f>0 on (0,1). We show that there is a positive cmin such that a traveling wave of speed c exists if and only if ccmin. Also, we show that traveling waves are unique up to a translation if f′(0)>0>f′(1) and g′(0)>0. The tails of traveling waves are also investigated.

Keywords

Discrete System Monostable Dynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Xinfu Chen
    • 1
  • Jong-Shenq Guo
    • 2
  1. 1.Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA (e-mail: xinfu@pitt.edu)US
  2. 2.Department of Mathematics, National Taiwan Normal University, Taipei 117, Taiwan (e-mail: jsguo@cc.ntnu.edu.tw)TW

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