On an elliptic system related to desertification studies
| dc.contributor.author | Díaz Díaz, Jesús Ildefonso | |
| dc.contributor.author | Kyriazopoulos, Paris | |
| dc.date.accessioned | 2023-06-19T13:28:44Z | |
| dc.date.available | 2023-06-19T13:28:44Z | |
| dc.date.issued | 2014 | |
| dc.description.abstract | In this communication, we consider the stationary problem of a non-linear parabolic system which arises in the context of dry-land vegetation. In the first part, we examine the existence and multiplicity of biomass stationary solutions, in terms of the precipitation rate parameter p, for a localized simplification of the system, with non-homogeneous rate of biomass loss. In fact, we show that under appropriate conditions on fixed parameters of the problem, multiple positive solutions exist for a range of the parameter p. In the second part, we consider the case of an idealized “oasis”, ω ⊂⊂ Ω, where we study the transition of the surface-water height in a neighborhood of the set ω | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Unión Europea. FP7 | |
| dc.description.sponsorship | Research Group MOMAT | |
| dc.description.sponsorship | UCM | |
| dc.description.sponsorship | DGISPI, Spain | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/28852 | |
| dc.identifier.doi | 10.1007/s13398-012-0108-0 | |
| dc.identifier.issn | 1578-7303 | |
| dc.identifier.officialurl | http://link.springer.com/article/10.1007%2Fs13398-012-0108-0#page-1 | |
| dc.identifier.relatedurl | http://lspringer.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/33820 | |
| dc.journal.title | RACSAM. Serie A. Matemáticas | |
| dc.language.iso | eng | |
| dc.page.final | 404 | |
| dc.page.initial | 397 | |
| dc.publisher | Springer | |
| dc.relation.projectID | ITN FIRST (238702) | |
| dc.relation.projectID | (910480) | |
| dc.relation.projectID | MTM2011-26119 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.9 | |
| dc.subject.keyword | Multiplicity of positive solutions | |
| dc.subject.keyword | Dry-land vegetation | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | On an elliptic system related to desertification studies | |
| dc.type | journal article | |
| dc.volume.number | 108 | |
| dcterms.references | Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18(4), 620–709 (1976) Ambrosetti, A., Malchiodi, A.: Nonlinear Analysis and Semilinear Elliptic Problems. Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (2007) Arcoya, D., Díaz, J.I., Tello, L.: S-shaped bifurcation branch in a quasilinear multivalued model arising in climatology. J. Differ. Equ. 149, 215–225 (1998) Dancer, E.N.: Global solution branches for positive mappings. Arch. Ration. Mech. Anal. 52, 181–192 (1973) Díaz, J.I.: Nonlinear Partial Differential Equations and Free Boundaries. Pitman, London (1985) Díaz, J.I., Hernández, J., Tello, L.: On the multiplicity of equilibrium solutions to a nonlinear diffusion equation on a manifold arising in climatology. Math. Anal. Appl. 216(AY975691), 593–613 (1997) Gilad, E., von Hardenberg, J., Provenzale, A., Shachak, M., Meron, E.: A mathematical model of plants as ecosystem engineers. J. Theor. Biol. 244, 680–691 (2007) Goto, Y., Hilhorst, D., Meron, E., Temam, R.: Existence theorem for a model of dryland vegetation. Discrete Continu. Dyn. Syst. Ser. B 16(1), 197–224 (2011) Goto, Y.: Global attractors for a vegetation model. Asymptot. Anal. 74, 75–94 (2011) Meron, E.: Modeling dryland landscapes. Math. Model. Nat. Phenom. 6(1), 163–187 (2011) Sherratt, J.A., Lord, G.J.: Nonlinear dynamics and pattern bifurcations in a model for vegetation stripes in semi-arid environments. Theor. Popul. Biol. 71, 1–11 (2007) Zeidler, E.: Nonlinear Functional Analysis and Its Applications, vol. II/B. Springer, Berlin (1990) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 | |
| relation.isAuthorOfPublication.latestForDiscovery | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 |
