Finite time and global existence for solutions to some singular reaction-diffusion systems
| dc.contributor.author | GAUCEL, S. | |
| hal.structure.identifier | Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | LANGLAIS, Michel | |
| dc.date.accessioned | 2024-04-04T03:03:10Z | |
| dc.date.available | 2024-04-04T03:03:10Z | |
| dc.date.issued | 2007 | |
| dc.identifier.issn | 1531-3492 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193047 | |
| dc.description.abstractEn | This note is dedicated to the question of global existence for so- lutions to a two component singular system of reaction–diffusion equations modeling predator–prey interactions in insular environments. Depending on a 2D parameter space, positive orbits of the underlying ODE system undergo interesting dynamics, e.g., finite time existence and global existence may co- exist. These results are partially extended to the reaction–diffusion system in the case of identical diffusivities. Our analysis relies on an auxiliary non singular reaction–diffusion system whose solutions may or may not blow up in finite time. Numerical simulations illustrate our analysis, including a numerical evidence of spatio–temporal oscillations. | |
| dc.language.iso | en | |
| dc.publisher | American Institute of Mathematical Sciences | |
| dc.subject.en | global existence | |
| dc.subject.en | blow–up time | |
| dc.subject.en | oscillations | |
| dc.subject.en | singular reaction–diffusion systems | |
| dc.subject.en | predator–prey model in insular environment | |
| dc.subject.en | invasion and persistence. | |
| dc.subject.en | invasion and persistence | |
| dc.title.en | Finite time and global existence for solutions to some singular reaction-diffusion systems | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Sciences du Vivant [q-bio]/Ecologie, Environnement/Ecosystèmes | |
| bordeaux.journal | Discrete and Continuous Dynamical Systems - Series B | |
| bordeaux.page | 61-72 | |
| bordeaux.volume | 8 | |
| 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-00195450 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00195450v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Discrete%20and%20Continuous%20Dynamical%20Systems%20-%20Series%20B&rft.date=2007&rft.volume=8&rft.spage=61-72&rft.epage=61-72&rft.eissn=1531-3492&rft.issn=1531-3492&rft.au=GAUCEL,%20S.&LANGLAIS,%20Michel&rft.genre=article |
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