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Article Dans Une Revue Nonlinear Analysis: Theory, Methods and Applications Année : 2005

Propagation speed of travelling fronts in non local reaction-diffusion equations

Jérôme Coville
Louis Dupaigne

Résumé

The object of this paper is to provide variational formulas characterizing the speed of travelling front solutions of the following nonlocal diffusion equation: partial derivativeu/partial derivativet = J * u - u + f(u), Where J is a dispersion kernel and f is any of the nonlinearities commonly used in various models ranging from combustion theory of ecology. In several situations, such as population dynamics, it is indeed natural to model the dispersion of a population using such operators. Furthermore, since travelling front solutions are expected to give the asymptotic behaviour in large time for solutions of the above equation, it is of the interest to characterize their speed. Our results. based on elementary techniques, generalize known results obtained for models involving local diffusion operators

Dates et versions

hal-02680665 , version 1 (31-05-2020)

Identifiants

Citer

Jérôme Coville, Louis Dupaigne. Propagation speed of travelling fronts in non local reaction-diffusion equations. Nonlinear Analysis: Theory, Methods and Applications, 2005, 60 (5), pp.797-819. ⟨10.1016/j.na.2003.10.030⟩. ⟨hal-02680665⟩
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