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Characterization of Traveling Waves Solutions to an Heterogeneous Diffusion Coupled System with Weak Advection

Author

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  • José Luis Díaz Palencia

    (Escuela Politécnica Superior, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1800, Pozuelo de Alarcón, 28223 Madrid, Spain)

Abstract

The aim of this work is to characterize Traveling Waves (TW) solutions for a coupled system with KPP-Fisher nonlinearity and weak advection. The heterogeneous diffusion introduces certain instabilities in the TW heteroclinic connections that are explored. In addition, a weak advection reflects the existence of a critical combined TW speed for which solutions are purely monotone. This study follows purely analytical techniques together with numerical exercises used to validate or extent the contents of the analytical principles. The main concepts treated are related to positivity conditions, TW propagation speed and homotopy representations to characterize the TW asymptotic behaviour.

Suggested Citation

  • José Luis Díaz Palencia, 2021. "Characterization of Traveling Waves Solutions to an Heterogeneous Diffusion Coupled System with Weak Advection," Mathematics, MDPI, vol. 9(18), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2300-:d:638087
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