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

The object of this paper is to provide variational formulas characterizing the speed of travelling front solutions of the following nonlocal diffusion equation:∂u∂t=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.