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



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.


Fractional laplacian Nonlinear Fisher-KPP reaction–diffusion equation Cooperative systems Time asymptotic propagation 

Mathematics Subject Classification

Primary 35R11 Secondary 35B40 



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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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institut de MathématiquesUniversité Paul SabatierToulouse Cedex 4France
  2. 2.Departamento de MatemáticaEscuela Politécnica NacionalQuitoEcuador

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