| dc.contributor.author | Gomez Serrano, Javier | |
| dc.contributor.author | Granero Belinchón, Rafael | |
| dc.contributor.other | Universidad de Cantabria | es_ES |
| dc.date.accessioned | 2023-08-02T08:14:31Z | |
| dc.date.available | 2023-08-02T08:14:31Z | |
| dc.date.issued | 2014-06 | |
| dc.identifier.issn | 0951-7715 | |
| dc.identifier.issn | 1361-6544 | |
| dc.identifier.other | MTM2011-26696 | es_ES |
| dc.identifier.uri | https://hdl.handle.net/10902/29577 | |
| dc.description.abstract | We exhibit a family of graphs that develop turning singularities (i.e. their Lipschitz seminorm blows up and they cease to be a graph, passing from the stable to the unstable regime) for the inhomogeneous, two-phase Muskat problem where the permeability is given by a nonnegative step function. We study the influence of different choices of the permeability and different boundary conditions (both at infinity and considering finite/infinite depth) in the development or prevention of singularities for short time. In the general case (inhomogeneous, confined) we prove a bifurcation diagram concerning the appearance or not of singularities when the depth of the medium and the permeabilities change. The proofs are carried out using a combination of classical analysis techniques and computer-assisted verification. | es_ES |
| dc.description.sponsorship | Acknowledgments: The authors are supported by the Grant MTM2011-26696 from Ministerio de Ciencia e Innovación (MICINN) and MINECO: ICMAT Severo Ochoa project SEV-2011- 0087. Javier Gómez-Serrano is supported by StG-203138CDSIF of the ERC. Rafael Granero-Belinchón is grateful to Luigi Berselli and Rafael Orive for productive comments in an early version of these results. Javier Gómez-Serrano thanks Rafael de la Llave for fruitful discussions. We thank Diego Córdoba for his guidance and useful suggestions. We wish to thank the Instituto de Ciencias Matemáticas (Madrid) for computing facilities. | es_ES |
| dc.format.extent | 30 p. | es_ES |
| dc.language.iso | eng | es_ES |
| dc.publisher | Institute of Physics | es_ES |
| dc.rights | © IOP Publishing Ltd & London Mathematical Society. This is an author-created, un-copyedited version of an article accepted for publication/published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/0951-7715/27/6/1471 | es_ES |
| dc.source | Nonlinearity, 2014, 27, 1471 | es_ES |
| dc.title | On turning waves for the inhomogeneous Muskat problem: a computer-assisted proof | es_ES |
| dc.type | info:eu-repo/semantics/article | es_ES |
| dc.relation.publisherVersion | https://doi.org/10.1088/0951-7715/27/6/1471 | es_ES |
| dc.rights.accessRights | openAccess | es_ES |
| dc.relation.projectID | info:eu-repo/grantAgreement/MICINN//MTM2011-26696/ES/ECUACIONES EN DERIVADAS PARCIALES QUE PROVIENEN DE LA MECANICA DE FLUIDOS/ | es_ES |
| dc.identifier.DOI | 10.1088/0951-7715/27/6/1471 | |
| dc.type.version | submittedVersion | es_ES |
