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Exponential Propagation for Fractional Reaction–Diffusion Cooperative Systems with Fast Decaying Initial Conditions

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Abstract

We study the time asymptotic propagation of solutions to the reaction–diffusion cooperative systems with fractional diffusion. We prove that the propagation speed is exponential in time, and we find the precise exponent of propagation. This exponent depends on the smallest index of the fractional laplacians and on the principal eigenvalue of the matrix DF(0) where F is the reaction term. We also note that this speed does not depend on the space direction.

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Acknowledgments

The research leading to these results has received funding from the European Research Council under the European Unions Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n.321186 - ReaDi -Reaction-Diffusion Equations, Propagation and Modeling. M. Y. was partially supported by Becas de Doctorado SENESCYT-Ecuador. The authors thank Professor J.-M. Roquejoffre for fruitful discussions and the anonymous referee for his/her comments, which resulted in a new version that gives more value to our results.

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Authors and Affiliations

  1. Institut de Mathématiques, Université Paul Sabatier, 118 Route de Narbonne, 31062, Toulouse Cedex 4, France

    Anne-Charline Coulon

  2. Departamento de Matemática, Escuela Politécnica Nacional, Ladrón de Guevara E11-253, Quito, Ecuador

    Miguel Yangari

Authors
  1. Anne-Charline Coulon
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  2. Miguel Yangari
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Correspondence to Miguel Yangari.

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Coulon, AC., Yangari, M. Exponential Propagation for Fractional Reaction–Diffusion Cooperative Systems with Fast Decaying Initial Conditions. J Dyn Diff Equat 29, 799–815 (2017). https://doi.org/10.1007/s10884-015-9479-1

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  • DOI: https://doi.org/10.1007/s10884-015-9479-1

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