Journal of Dynamics and Differential Equations

, Volume 21, Issue 4, pp 663–680

Monotone Wavefronts for Partially Degenerate Reaction-Diffusion Systems

Article

Abstract

This paper is devoted to the study of monotone wavefronts for cooperative and partially degenerate reaction-diffusion systems. The existence of monostable wavefronts is established via the vector-valued upper and lower solutions method. It turns out that the minimal wave speed of monostable wavefronts coincides with the spreading speed. The existence of bistable wavefronts is obtained by the vanishing viscosity approach combined with the properties of spreading speeds in the monostable case.

Keywords

Degenerate reaction-diffusion systems Spreading speeds Monostable and bistable wavefronts Minimal wave speeds 

Mathematics Subject Classification (2000)

35K57 35B40 35B20 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinChina
  2. 2.Department of Mathematics and StatisticsMemorial University of NewfoundlandSt. John’sCanada

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