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