A singular reaction-diffusion system modelling prey-predator interactions : Invasion and co-extinction waves
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DUCROT, Arnaud | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | LANGLAIS, Michel | |
| dc.date.accessioned | 2024-04-04T02:24:57Z | |
| dc.date.available | 2024-04-04T02:24:57Z | |
| dc.date.created | 2011 | |
| dc.date.issued | 2012 | |
| dc.identifier.issn | 0022-0396 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189850 | |
| dc.description.abstractEn | We consider a singular reaction-diffusion system arising in modelling prey-predator interactions in a fragile environment. Since the underlying ODEs system exhibits a complex dynamics including possible finite time quenching, one first provides a suitable notion of global travelling wave weak solution. Then our study focusses on the existence of travelling waves solutions for predator invasion in such environments. We devise a regularized problem to prove the existence of travelling wave solutions for predator invasion followed by a possible co-extinction tail for both species. Under suitable assumptions on the diffusion coefficients and on species growth rates we show that travelling wave solutions are actually positive on a half line and identically zero elsewhere, such a property arising for every admissible wave speeds. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | Singular reaction-diffusion system \sep Travelling waves \sep Finite time extinction | |
| dc.title.en | A singular reaction-diffusion system modelling prey-predator interactions : Invasion and co-extinction waves | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.jde.2012.04.005 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Journal of Differential Equations | |
| bordeaux.page | 502-532 | |
| bordeaux.volume | 253 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00710405 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00710405v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Differential%20Equations&rft.date=2012&rft.volume=253&rft.spage=502-532&rft.epage=502-532&rft.eissn=0022-0396&rft.issn=0022-0396&rft.au=DUCROT,%20Arnaud&LANGLAIS,%20Michel&rft.genre=article |
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