Travelling waves for a non-monotone bistable equation with delay: existence and oscillations
| hal.structure.identifier | Institut Montpelliérain Alexander Grothendieck [IMAG] | |
| dc.contributor.author | ALFARO, Matthieu | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DUCROT, Arnaud | |
| hal.structure.identifier | Institut Élie Cartan de Lorraine [IECL] | |
| dc.contributor.author | GILETTI, Thomas | |
| dc.date.accessioned | 2024-04-04T03:11:41Z | |
| dc.date.available | 2024-04-04T03:11:41Z | |
| dc.date.issued | 2018 | |
| dc.identifier.issn | 0024-6115 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193797 | |
| dc.description.abstractEn | We consider a bistable ($0<\theta<1$ being the three constant steady states) delayed reaction diffusion equation, which serves as a model in population dynamics. The problem does not admit any comparison principle. This prevents the use of classical technics and, as a consequence, it is far from obvious to understand the behaviour of a possible travelling wave in $+\infty$. Combining refined {\it a priori} estimates and a Leray Schauder topological degree argument, we construct a travelling wave connecting 0 in $-\infty$ to \lq\lq something'' which is strictly above the unstable equilibrium $\theta$ in $+\infty$. Furthemore, we present situations (additional bound on the nonlinearity or small delay) where the wave converges to 1 in $+\infty$, whereas the wave is shown to oscillate around 1 in $+\infty$ when, typically, the delay is large. | |
| dc.language.iso | en | |
| dc.publisher | London Mathematical Society | |
| dc.title.en | Travelling waves for a non-monotone bistable equation with delay: existence and oscillations | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1112/plms.12092 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 1701.06394 | |
| bordeaux.journal | Proceedings of the London Mathematical Society | |
| bordeaux.page | 729-759 | |
| bordeaux.volume | 116 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01443282 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01443282v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Proceedings%20of%20the%20London%20Mathematical%20Society&rft.date=2018&rft.volume=116&rft.issue=4&rft.spage=729-759&rft.epage=729-759&rft.eissn=0024-6115&rft.issn=0024-6115&rft.au=ALFARO,%20Matthieu&DUCROT,%20Arnaud&GILETTI,%20Thomas&rft.genre=article |
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