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.
Pulsating solutions for multidimensional bistable and multistable equations / Giletti, T.; Rossi, L.. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 378:3-4(2020), pp. 1555-1611. [10.1007/s00208-019-01919-z]
Pulsating solutions for multidimensional bistable and multistable equations
Rossi L.
2020
Abstract
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.File | Dimensione | Formato | |
---|---|---|---|
Giletti_preprint_Pulsating-solutions_2020.pdf
accesso aperto
Tipologia:
Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza:
Creative commons
Dimensione
604.77 kB
Formato
Adobe PDF
|
604.77 kB | Adobe PDF | |
Giletti_Pulsating-solutions_2020.pdf
solo gestori archivio
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
694.23 kB
Formato
Adobe PDF
|
694.23 kB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.