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* Corresponding author 1 CAMS - Centre d-analyse et de mathématique sociale 2 LATP - Laboratoire d-Analyse, Topologie, Probabilités

Abstract : In the article of H. Berestycki and F. Hamel, On a general definition of transition waves, there is a generalization of the classical definition of a transition wave in Euclidean spaces e.g. a traveling wave or an invasive front to the case where the level sets of the wave are no longer planes but surfaces. We will prove that the same results and properties on general transition waves that appear in the cited article hold in the case of a non-compact complete Riemannian manifold, namely: 1 the wave is associated to a generalized front, which moves -close- to the level sets of the wave; 2 there is a mean propagation speed of the wave, which is independent of the choice of the associated front; 3 in the case of an invasion the wave is an increasing function in time.

Keywords : complete Riemannian manifolds traveling waves Reaction-diffusion equations parabolic equations on manifolds complete Riemannian manifolds.

Author: Henri Berestycki - Mauricio Labadie - François Hamel -



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