DUCROT, Arnaud; LANGLAIS, Michel

doi:10.1016/j.jde.2012.04.005

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DUCROT, Arnaud
Institut de Mathématiques de Bordeaux [IMB]

LANGLAIS, Michel
Institut de Mathématiques de Bordeaux [IMB]

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Journal of Differential Equations. 2012, vol. 253, p. 502-532

Elsevier

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We consider a singular reaction-diffusion system arising in modelling prey-predator interactions in a fragile environment. Since the underlying ODEs system exhibits a complex dynamics including possible finite time quenching, one first provides a suitable notion of global travelling wave weak solution. Then our study focusses on the existence of travelling waves solutions for predator invasion in such environments. We devise a regularized problem to prove the existence of travelling wave solutions for predator invasion followed by a possible co-extinction tail for both species. Under suitable assumptions on the diffusion coefficients and on species growth rates we show that travelling wave solutions are actually positive on a half line and identically zero elsewhere, such a property arising for every admissible wave speeds.< Leer menos

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Singular reaction-diffusion system \sep Travelling waves \sep Finite time extinction

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A singular reaction-diffusion system modelling prey-predator interactions : Invasion and co-extinction waves

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