The sub-supertrajectory method. Application to the nonautonomous competition Lotka-Volterra model
| dc.contributor.author | Langa, J.A. | |
| dc.contributor.author | Rodríguez Bernal, Aníbal | |
| dc.contributor.author | Suárez, Antonio | |
| dc.date.accessioned | 2023-06-20T03:58:47Z | |
| dc.date.available | 2023-06-20T03:58:47Z | |
| dc.date.issued | 2010 | |
| dc.description.abstract | In this paper we study in detail the pullback and forwards attractions to non-autonomous competition Lotka-Volterra system. In particular, under some conditions on the parameters, we prove the existence of a unique non-degenerate global solution for these models, which attracts any other complete bounded trajectory. For that we present the sub-supertrajectory tool as a generalization of the now classical subsupersolution method. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | CCG07-UCM/ESP-2393 | |
| dc.description.sponsorship | UCM-CAM | |
| dc.description.sponsorship | CADEDIF | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/33328 | |
| dc.identifier.issn | 1575-9822 | |
| dc.identifier.officialurl | http://www.sema.org.es/web/component/option,com_wrapper/Itemid,68/lang,spanish/ | |
| dc.identifier.relatedurl | http://www.sema.org.es/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/44757 | |
| dc.journal.title | Boletín de la Sociedad Española de Matemática Aplicada. SEMA | |
| dc.language.iso | eng | |
| dc.page.final | 99 | |
| dc.page.initial | 91 | |
| dc.publisher | Sociedad Española de Matemática Aplicada | |
| dc.relation.projectID | MTM2008-0088 | |
| dc.relation.projectID | HF2008-0039 | |
| dc.relation.projectID | PHB2006-003PC | |
| dc.relation.projectID | MTM2006-08262 | |
| dc.relation.projectID | MTM2006-07932 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517.9 | |
| dc.subject.keyword | Sub-supertrajectory method | |
| dc.subject.keyword | Lotka-Volterra competition system | |
| dc.subject.keyword | attracting complete trajectories | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | The sub-supertrajectory method. Application to the nonautonomous competition Lotka-Volterra model | |
| dc.type | journal article | |
| dc.volume.number | 51 | |
| dcterms.references | R. S. Cantrell and C. Cosner, Practical persistence in ecological models via comparison methods, Proc. Royal Soc. Edin., 126A (1996) 247-272. R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, John Wiley & Sons. Ltd. 2003. I. Chueshov, Monotone random systems theory and applications. Lecture Notes in Mathematics, 1779. Springer-Verlag, Berlin, 2002. P. Hess, Periodic-Parabolic boundary value problems and positivity, Pitman Research Notes in Mathematics 247, Harlow Longman. 1991. G. Hetzer, W. Shen, Uniform persistence, coexistence, and extinction in almost periodic/nonautonomous competition diffusion systems, SIAM J. Math. Anal., 34 (2002) 204-221. J. A. Langa, J.C. Robinson, A. Rodríguez-Bernal and A. Suárez, Permanence and asymptotically stable complete trajectories for nonautonomous Lotka-Volterra models with diffusion, SIAM J. Math. Anal. 40 (2009) 2179–2216. J. A. Langa, A. Rodríguez-Bernal and A. Suárez, On the long time behaviour of non-autonomous Lotka-Volterra models with diffusion via the sub-super trajectory method, submitted. J. A. Langa and A. Suárez, Pullback permanence for non-autonomous partial differential equations, Electron. J. Differential Equations 2002, 72, 20 pp. J. López-Gómez, On the structure of the permanence region for competing species models with general diffusivities and transport effects,Discrete Contin. Dyn. Syst., 2 (1996) 525-542. C. V. Pao, Nonlinear parabolic and elliptic equations, Plenum, New York, 1992. J.C. Robinson, A. Rodríguez-Bernal, and A. Vidal-López, Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems, J. Differential Equations 238 (2007) 289–337. A. Rodríguez-Bernal and A. Vidal-López, Existence, uniqueness and attractivity properties of positive complete trajectories for non-autonomous reaction-diffusion problems, Discrete Contin. Dyn. Syst., 18 (2007) 537–567 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 | |
| relation.isAuthorOfPublication.latestForDiscovery | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 |
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