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BIRS Workshop Lecture Videos

Propagating terraces in multidimensional and spatially periodic domains Giletti, Thomas


This talk will be devoted to the existence of pulsating travelling front solutions for spatially periodic heterogeneous reaction-diffusion equations in arbitrary dimension, in the multistable case. In general, the notion of a single front is not sufficient to understand the dynamics of solutions, and we instead observe the appearance of a so-called propagating terrace. This roughly refers to a finite family of stacked fronts connecting intermediate stable steady states and whose speeds are ordered. Surprisingly, for a given equation, the shape of this terrace (i.e., the involved intermediate steady states or even their number) may depend on the direction of the propagation. This in turn raises some difficulties in the spreading shape of solutions of the evolution problem. The presented results come from a series of collaborations with W. Ding, A. Ducrot, H. Matano and L. Rossi.

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