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| The standard notions of reaction-diffusion waves and fronts can be viewed as examples of generalized transition waves. These notions involve uniform limits, with respect to the geodesic distance, to a family of hypersurfaces which are parametrized by time. The existence of transition waves has been proved in various contexts where the standard notions of waves make no longer sense. Even for homogeneous equations, fronts with various non-planar shapes or with varying speeds are known to exist. In this talk, I will report on some recent existence results and qualitative properties of transition fronts for monostable and bistable homogeneous and heterogeneous equations. I will also discuss their mean speed of propagation. |
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