Traveling wave solutions to some reaction diffusion equations with fractional Laplacians

  • Changfeng GuiEmail author
  • Tingting Huan


We show the nonexistence of traveling wave solutions in the combustion model with fractional Laplacian \(\displaystyle (-\Delta )^s\) when \(\displaystyle s\in (0,1/2]\). Our method can be used to give a direct and simple proof of the nonexistence of traveling fronts for the usual Fisher-KPP nonlinearity. Also we prove the existence and nonexistence of traveling wave solutions for different ranges of the fractional power \(s\) for the generalized Fisher–KPP type model.

Mathematics Subject Classification

primary 35B32 35C07 35J20 35R09 35R11 45G05 47G10 



This work was partially supported by a grant from the Simons Foundation (Award # 199305) and a NSF IPA award. The authors would also like to thank the anonymous referee for helpful suggesions for the revision of the manuscript.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ConnecticutStorrsUSA

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