%0 Journal Article %T Bistable travelling waves for nonlocal reaction diffusion equations %A Matthieu Alfaro %A Jerome Coville %A Gael Raoul %J Mathematics %D 2013 %I arXiv %X We are concerned with travelling wave solutions arising in a reaction diffusion equation with bistable and nonlocal nonlinearity, for which the comparison principle does not hold. Stability of the equilibrium $u\equiv 1$ is not assumed. We construct a travelling wave solution connecting 0 to an unknown steady state, which is "above and away", from the intermediate equilibrium. For focusing kernels we prove that, as expected, the wave connects 0 to 1. Our results also apply readily to the nonlocal ignition case. %U http://arxiv.org/abs/1303.3554v1