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Remarks about spatially structured SI model systems with cross diffusion
hal.structure.identifier | Universidad del Bio Bio [Concepción] [UBB] | |
dc.contributor.author | ANAYA, Veronica | |
hal.structure.identifier | Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN] | |
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | BENDAHMANE, Mostafa | |
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | LANGLAIS, Michel | |
hal.structure.identifier | Departamento de Ingeniería Matemática [Santiago] [DIM] | |
dc.contributor.author | SEPULVEDA, Mauricio | |
dc.contributor.editor | B. N. Chetverushki | |
dc.contributor.editor | W. Fitzgibbon | |
dc.contributor.editor | Y.A. Kuznetsov | |
dc.contributor.editor | P. Neittaanmäki | |
dc.contributor.editor | J. Periaux | |
dc.contributor.editor | O. Pironneau | |
dc.date.accessioned | 2024-04-04T03:00:57Z | |
dc.date.available | 2024-04-04T03:00:57Z | |
dc.date.created | 2019 | |
dc.date.issued | 2019 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192858 | |
dc.description.abstractEn | One of the simplest deterministic mathematical model for the spread of an epidemic disease is the so-called SI system made of two Ordinary Differential Equations. It exhibits simple dynamics: a bifurcation parameter T0 yielding persistence of the disease when T0>1, else extinction occurs. A natural question is whether this gentle dynamic can be disturbed by spatial diffusion. It is straightforward to check it is not feasible for linear/nonlinear diffusions. When cross diffusion is introduced for suitable choices of the parameter data set this persistent state of the ODE model system becomes linearly unstable for the resulting initial and no-flux boundary value problem. On the other hand “natural” weak solutions can be defined for this initial and no-flux boundary value problem and proved to exist provided nonlinear and cross diffusivities satisfy some constraints. These constraints are not fully met for the parameter data set yielding instability. A remaining open question is: to which solutions does this apply? Periodic behaviors are observed for a suitable range of cross diffusivities. | |
dc.language.iso | en | |
dc.publisher | Springer | |
dc.source.title | Contributions to Partial Differential Equations and Applications | |
dc.title.en | Remarks about spatially structured SI model systems with cross diffusion | |
dc.type | Chapitre d'ouvrage | |
dc.identifier.doi | 10.1007/978-3-319-78325-3_5 | |
dc.subject.hal | Mathématiques [math] | |
dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
dc.subject.hal | Mathématiques [math]/Combinatoire [math.CO] | |
dc.subject.hal | Sciences du Vivant [q-bio] | |
bordeaux.page | 21 | |
bordeaux.volume | 47 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
bordeaux.title.proceeding | Contributions to Partial Differential Equations and Applications | |
hal.identifier | hal-02142018 | |
hal.version | 1 | |
hal.popular | oui | |
hal.audience | Internationale | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-02142018v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=Contributions%20to%20Partial%20Differential%20Equations%20and%20Applications&rft.date=2019&rft.volume=47&rft.spage=21&rft.epage=21&rft.au=ANAYA,%20Veronica&BENDAHMANE,%20Mostafa&LANGLAIS,%20Michel&SEPULVEDA,%20Mauricio&rft.genre=unknown |
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