Journal
MATHEMATISCHE ANNALEN
Volume 378, Issue 3-4, Pages 1555-1611Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00208-019-01919-z
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Funding
- European Research Council [321186]
- Agence Nationale de la Recherche [ANR-14-CE25-0013]
- European Research Council (ERC) [321186] Funding Source: European Research Council (ERC)
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We investigate the existence of pulsating front-like solutions for spatially periodic heterogeneous reaction-diffusion equations in arbitrary dimension, in both bistable and more general multistable frameworks. In the multistable case, 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 whose speeds are ordered. Surprisingly, for a given equation, the shape of this terrace (i.e., the involved intermediate states or even the cardinality of the family of fronts) may depend on the direction of propagation.
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