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Monotone Wavefronts for Partially Degenerate Reaction-Diffusion Systems

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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.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    Jian Fang

  2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S7, Canada

    Jian Fang & Xiao-Qiang Zhao

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  1. Jian Fang
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  2. Xiao-Qiang Zhao
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Correspondence to Xiao-Qiang Zhao.

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Fang, J., Zhao, XQ. Monotone Wavefronts for Partially Degenerate Reaction-Diffusion Systems. J Dyn Diff Equat 21, 663–680 (2009). https://doi.org/10.1007/s10884-009-9152-7

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  • DOI: https://doi.org/10.1007/s10884-009-9152-7

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