A nonlinear bilaplacian equation with hinged boundary conditions and very weak solutions: analysis and numerical solution
| dc.contributor.author | Arregui, Iñigo | |
| dc.contributor.author | Díaz Díaz, Jesús Ildefonso | |
| dc.date.accessioned | 2023-06-19T13:28:40Z | |
| dc.date.available | 2023-06-19T13:28:40Z | |
| dc.date.issued | 2014 | |
| dc.description.abstract | We study linear and nonlinear bilaplacian problems with hinged boundary conditions and right hand side in L1( : δ), with δ = dist(x, ∂). More precisely, the existence and uniqueness of the very weak solution is obtained and some numerical techniques are proposed for its approximation. | |
| 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 | MCINN of Spain | |
| dc.description.sponsorship | Xunta de Galicia | |
| dc.description.sponsorship | DGISPI of Spain | |
| dc.description.sponsorship | Research Group MOMAT | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/28848 | |
| dc.identifier.doi | 10.1007/s13398-013-0148-0 | |
| dc.identifier.issn | 1578-7303 | |
| dc.identifier.officialurl | http://link.springer.com/article/10.1007%2Fs13398-013-0148-0#page-1 | |
| dc.identifier.relatedurl | http://link.springer.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/33817 | |
| dc.journal.title | RACSAM. Serie A. Matemáticas | |
| dc.language.iso | eng | |
| dc.page.final | 879 | |
| dc.page.initial | 867 | |
| dc.publisher | Springer | |
| dc.relation.projectID | FIRST (238702) | |
| dc.relation.projectID | MTM2010–21135–C02–01 | |
| dc.relation.projectID | 910480 | |
| dc.relation.projectID | MTM2011-26119) | |
| dc.relation.projectID | Ayuda CN2011/004 cofunded with FEDE | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517.9 | |
| dc.subject.keyword | Very weak solutions | |
| dc.subject.keyword | Distance to the boundary | |
| dc.subject.keyword | Nonlinear bilaplacian operator | |
| dc.subject.keyword | Hinged boundary conditions | |
| dc.subject.keyword | Numerical methods | |
| dc.subject.keyword | Finite elements | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | A nonlinear bilaplacian equation with hinged boundary conditions and very weak solutions: analysis and numerical solution | |
| dc.type | journal article | |
| dc.volume.number | 108 | |
| dcterms.references | Bayada, G., Durany, J., Vázquez, C.: Existence of a solution for a lubrication problem in elastic journal bearing devices with thin bearing. Math. Methods Appl. Sci. 18, 255–266 (1995) Brezis, H.: Une équation Semi-linéaire Avec Conditions Aux Limites Dans L1. Personal communication to J.I. Díaz (unpublished) Brezis, H., Cabré, X.: Some simple nonlinear PDE’s without solutions. Bull. UMI 1, 223–262 (1998) Brezis, H., Cazenave, T., Martel, Y., Ramiandrisoa, A.: Blow up for ut − �u = g(u) revisited. Adv.Differ. Equ. 1, 73–90 (1996) Casado-Díaz, J., Chacón-Rebollo, T., Girault, V., Gómez-Mármol, M., Murat, F.: Finite elements approximation of second order linear elliptic equations in divergence form with right-hand side in L1. Numer.Math. 105, 337–374 (2007) Crandall, M.G., Tartar, L.: Some relations between nonexpansive and order preserving maps. Proc. AMS 78(3), 385–390 (1980) Díaz, J.I.: On the very weak solvability of the beam equation. Rev. R. Acad. Cien. Ser. A (RACSAM) 105, 167–172 (2011) Díaz, J.I.: Non Hookean Beams and Plates: Very Weak Solutions and Their Numerical Analysis (2013).(submitted) Díaz, J.I., Hernández, J., Rakotoson, J.M.: On very weak positive solutions to some semilinear elliptic problems with simultaneous singular nonlinear and spatial dependence terms. Milan J. Math. 79, 233–245(2011) Díaz, J.I., Rakotoson, J.M.: On the differentiability of very weak solutions with right hand side data integrable with respect to the distance to the boundary. J. Funct.Anal. 257, 807–831 (2009) Díaz, J.I., Rakotoson, J.M.: On very weak solutions of semi-linear elliptic equations in the framework of weighted spaces with respect to the distance to the boundary. Discret. Contin. Dyn. Syst. 27, 1037–1058 (2010) Durany, J., García, G., Vázquez, C.: An elastohydrodynamic coupled problem between a piezoviscous Reynolds equation and a hinged plate model. RAIRO Modél. Math. Anal. Numér. 31, 495–516 (1997) Friedman, A.: Generalized Functions and Partial Differential Equations. Prentice-Hall, Englewood Cliffs (1963) Ghergu, M.: A biharmonic equation with singular nonlinearity. Proc. Edinb. Math. Soc. 55, 155–166(2012) Souplet, Ph.: A survey on L p δ spaces and their applications to nonlinear elliptic and parabolic problems. Nonlinear partial differential equations and their applications. GAKUTO Int. Ser. Math. Sci. Appl. 20,464–479 (2004) Stakgold, I.: Green’s functions and boundary value problems. In: Pure and Applied Mathematics Series. Wiley, New York (1998) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 | |
| relation.isAuthorOfPublication.latestForDiscovery | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 |
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