Bifurcation to locked fronts in two component reaction–diffusion systems
Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 2, pp. 545-584.
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We study invasion fronts and spreading speeds in two component reaction–diffusion systems. Using a variation of Lin's method, we construct traveling front solutions and show the existence of a bifurcation to locked fronts where both components invade at the same speed. Expansions of the wave speed as a function of the diffusion constant of one species are obtained. The bifurcation can be sub or super-critical depending on whether the locked fronts exist for parameter values above or below the bifurcation value. Interestingly, in the sub-critical case numerical simulations reveal that the spreading speed of the PDE system does not depend continuously on the coefficient of diffusion.

DOI : 10.1016/j.anihpc.2018.08.001
Mots-clés : Invasion fronts, Spreading speeds, Lin's method 
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Faye, Grégory; Holzer, Matt. Bifurcation to locked fronts in two component reaction–diffusion systems. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 2, pp. 545-584. doi : 10.1016/j.anihpc.2018.08.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2018.08.001/

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