Pulsating solutions for multidimensional bistable and multistable\n equations

Abstract

We devote this paper to the issue of existence of pulsating travelling front\nsolutions for spatially periodic heterogeneous reaction-diffusion equations in\narbitrary dimension, in both bistable and more general multistable frameworks.\nIn the multistable case, the notion of a single front is not sufficient to\nunderstand the dynamics of solutions, and we instead observe the appearance of\na so-called propagating terrace. This roughly refers to a finite family of\nstacked fronts connecting intermediate stable steady states whose speeds are\nordered. Surprisingly, for a given equation, the shape of this terrace (i.e.,\nthe involved intermediate states or even the cardinality of the family of\nfronts) may depend on the direction of propagation.\n