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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2017

Transition fronts and stretching phenomena for a general class of reaction-dispersion equations

Jimmy Garnier
François Hamel
Lionel Roques

Résumé

We consider a general form of reaction-dispersion equations with non-local dispersal and local reaction. Under some general conditions, we prove the non-existence of transition fronts, as well as some stretching properties at large time for the solutions of the Cauchy problem. These conditions are satisfied in particular when the reaction is monostable and when the dispersal operator is either the fractional Laplacian, a convolution operator with a fat-tailed kernel or a nonlinear fast diffusion operator.
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Dates et versions

hal-01142200 , version 1 (10-06-2015)

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Jimmy Garnier, François Hamel, Lionel Roques. Transition fronts and stretching phenomena for a general class of reaction-dispersion equations. Discrete and Continuous Dynamical Systems - Series A, 2017, 37 (2), pp.743 - 756. ⟨10.3934/dcds.2017031⟩. ⟨hal-01142200⟩
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