| Abstract: |
| Travelling fronts typically connect two stationary states of a reaction-diffusion equation and often accurately describe the large-time behavior of solutions. However, when many such steady states exist, a more complicated dynamics may appear involving a layer of several fronts, or propagating terrace. In this talk, we will consider a spatially periodic problem of the multistable type, where the equation admits a finite sequence of ordered stable steady states. In this rather general context, we will show that a propagating terrace exists in any direction. Our approach relies on an abstract discrete framework together with an iterative argument. Surprisingly, due to the loss of symmetry induced by the heterogeneity, the shape of the propagating terrace may differ depending on the direction. In particular, travelling waves may exist only in some directions. This is a joint work with Luca Rossi from EHESS. |
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