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Pré-Publication, Document De Travail Année : 2018

Invasion of an empty habitat by two competitors: spreading properties of monostable two-species competition--diffusion systems

Résumé

This paper is concerned with some spreading properties of monos-table Lotka–Volterra two-species competition–diffusion systems when the initial values are null or exponentially decaying in a right half-line. Thanks to a careful construction of super-solutions and sub-solutions, we improve previously known results and settle open questions. In particular, we show that if the weaker competitor is also the faster one, then it is able to evade the stronger and slower competitor by invading first into unoccupied territories. The pair of speeds depends on the initial values. If these are null in a right half-line, then the first speed is the KPP speed of the fastest competitor and the second speed is given by an exact formula depending on the first speed and on the minimal speed of traveling waves connecting the two semi-extinct equilibria. Furthermore, the unbounded set of pairs of speeds achievable with exponentially decaying initial values is characterized, up to a negligible set.
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Dates et versions

hal-01718928 , version 1 (27-02-2018)
hal-01718928 , version 2 (09-03-2018)
hal-01718928 , version 3 (08-05-2018)
hal-01718928 , version 4 (02-07-2018)
hal-01718928 , version 5 (04-04-2019)

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Léo Girardin, King-Yeung Lam. Invasion of an empty habitat by two competitors: spreading properties of monostable two-species competition--diffusion systems. 2018. ⟨hal-01718928v4⟩
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