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Pré-Publication, Document De Travail Année : 2007

Travelling fronts in asymmetric nonlocal reaction diffusion equations: The bistable and ignition cases

Jérôme Coville

Résumé

This paper is devoted to the study of the travelling front solutions which appear in a nonlocal reaction-diffusion equations of the form $$\frac{\partial u}{\partial t}=\j\star u -u +f(u).$$ When the nonlinearity $f$ is of bistable or ignition type, and the dispersion kernel $\j$ is asymmetric, the existence of a travelling wave is proved. The uniqueness of the speed of the front is also established. The construction of the front essentially relies on the vanishing viscosity techniques, some a priori estimates on the speed's front and various comparison principles.
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Dates et versions

hal-00696208 , version 1 (11-05-2012)

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  • HAL Id : hal-00696208 , version 1

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Jérôme Coville. Travelling fronts in asymmetric nonlocal reaction diffusion equations: The bistable and ignition cases. 2007. ⟨hal-00696208⟩
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