A nonlinear bilaplacian equation with hinged boundary conditions and very weak solutions: analysis and numerical solution

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dc.contributor.authorArregui, I.
dc.contributor.authorDíaz Díaz, Jesús Ildefonso
dc.date.accessioned2023-06-19T13:28:40Z
dc.date.available2023-06-19T13:28:40Z
dc.date.issued2014
dc.description.abstractWe 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.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipUnión Europea. FP7
dc.description.sponsorshipMCINN of Spain
dc.description.sponsorshipXunta de Galicia
dc.description.sponsorshipDGISPI of Spain
dc.description.sponsorshipResearch Group MOMAT
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/28848
dc.identifier.citationBayada, 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 Personal communication to J.I. Díaz (unpublished) Brezis, H., Cabré, X.: Some simple nonlinear PDE’s without solutions.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)
dc.identifier.doi10.1007/s13398-013-0148-0
dc.identifier.issn1578-7303
dc.identifier.officialurlhttp://link.springer.com/article/10.1007%2Fs13398-013-0148-0#page-1
dc.identifier.relatedurlhttp://link.springer.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/33817
dc.journal.titleRACSAM. Serie A. Matemáticas
dc.language.isoeng
dc.page.final879
dc.page.initial867
dc.publisherSpringer
dc.relation.projectIDFIRST (238702)
dc.relation.projectIDMTM2010–21135–C02–01
dc.relation.projectID910480
dc.relation.projectIDMTM2011-26119)
dc.relation.projectIDAyuda CN2011/004 cofunded with FEDE
dc.rights.accessRightsopen access
dc.subject.cdu517.9
dc.subject.keywordVery weak solutions
dc.subject.keywordDistance to the boundary
dc.subject.keywordNonlinear bilaplacian operator
dc.subject.keywordHinged boundary conditions
dc.subject.keywordNumerical methods
dc.subject.keywordFinite elements
dc.subject.ucmEcuaciones diferenciales
dc.subject.unesco1202.07 Ecuaciones en Diferencias
dc.titleA nonlinear bilaplacian equation with hinged boundary conditions and very weak solutions: analysis and numerical solution
dc.typejournal article
dc.volume.number108
dspace.entity.typePublication
relation.isAuthorOfPublication34ef57af-1f9d-4cf3-85a8-6a4171b23557
relation.isAuthorOfPublication.latestForDiscovery34ef57af-1f9d-4cf3-85a8-6a4171b23557
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