This paper is a continuation of Berestycki et al (2013 J. Math. Biol. 66 743-66) where a new model of biological invasions in the plane directed by a line was introduced. Here we include new features such as transport and reaction terms on the line. Their interaction with the pure diffusivity in the plane is quantified in terms of enhancement of the propagation speed. We establish conditions that determine whether the spreading speed exceeds the standard Fisher-KPP invasion speed. These conditions involve the ratio of the diffusivities on the line and in the field, the transport term and the reactions. We derive the asymptotic behaviour for large diffusions or large transports. We also discuss the biological interpretation of these findings. © 2013 IOP Publishing Ltd & London Mathematical Society.

Fisher-KPP propagation in the presence of a line: Further effects / Berestycki, H.; Roquejoffre, J. -M.; Rossi, L.. - In: NONLINEARITY. - ISSN 0951-7715. - 26:9(2013), pp. 2623-2640. [10.1088/0951-7715/26/9/2623]

Fisher-KPP propagation in the presence of a line: Further effects

Rossi L.
2013

Abstract

This paper is a continuation of Berestycki et al (2013 J. Math. Biol. 66 743-66) where a new model of biological invasions in the plane directed by a line was introduced. Here we include new features such as transport and reaction terms on the line. Their interaction with the pure diffusivity in the plane is quantified in terms of enhancement of the propagation speed. We establish conditions that determine whether the spreading speed exceeds the standard Fisher-KPP invasion speed. These conditions involve the ratio of the diffusivities on the line and in the field, the transport term and the reactions. We derive the asymptotic behaviour for large diffusions or large transports. We also discuss the biological interpretation of these findings. © 2013 IOP Publishing Ltd & London Mathematical Society.
2013
Population dynamics; Fisher-KPP equation; fast diffusion line; transport term
01 Pubblicazione su rivista::01a Articolo in rivista
Fisher-KPP propagation in the presence of a line: Further effects / Berestycki, H.; Roquejoffre, J. -M.; Rossi, L.. - In: NONLINEARITY. - ISSN 0951-7715. - 26:9(2013), pp. 2623-2640. [10.1088/0951-7715/26/9/2623]
File allegati a questo prodotto
File Dimensione Formato  
Berestychi_preprint_Fisher-KPP-propagation_2013.pdf

accesso aperto

Tipologia: Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza: Creative commons
Dimensione 375.51 kB
Formato Adobe PDF
375.51 kB Adobe PDF
Berestychi_Fisher-KPP-propagation_2013.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 278.97 kB
Formato Adobe PDF
278.97 kB Adobe PDF   Contatta l'autore

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1464895
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 29
  • ???jsp.display-item.citation.isi??? 26
social impact