Geodesic
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
Keywords: Invasion fronts, Spreading speeds, Lin's method 
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     title = {Bifurcation to locked fronts in two component reaction{\textendash}diffusion systems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {545--584},
     year = {2019},
     publisher = {Elsevier},
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     number = {2},
     doi = {10.1016/j.anihpc.2018.08.001},
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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

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