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

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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

Abstract

We study linear and nonlinear bilaplacian problems with hinged boundary conditions and right hand side in \(L^{1}(\Omega :\delta )\), with \(\delta =\text{ dist }\,(x,\partial \Omega )\). More precisely, the existence and uniqueness of the very weak solution is obtained and some numerical techniques are proposed for its approximation.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Informatics, University of A Coruña, Campus Elviña s/n, 15071 , Coruña, Spain

    Iñigo Arregui & Carlos Vázquez

  2. Department of Applied Mathematics, Instituto de Matemática Interdisciplinar, Complutense University of Madrid, Plaza de las Ciencias 3, 28040 , Madrid, Spain

    Jesús Ildefonso Díaz

Authors
  1. Iñigo Arregui
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  2. Jesús Ildefonso Díaz
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  3. Carlos Vázquez
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Corresponding author

Correspondence to Carlos Vázquez.

Additional information

I. Arregui and C. Vázquez have been partially funded by MCINN of Spain (Project MTM2010–21135–C02–01) and Xunta de Galicia (Ayuda CN2011/004 cofunded with FEDER). J. I. Díaz has been partially supported by DGISPI of Spain (Project MTM2011-26119), the Research Group MOMAT (Ref. 910480) supported by UCM and ITN FIRST of the Seventh Framework Program of the European Community’s (Grant agreement 238702).

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Arregui, I., Díaz, J.I. & Vázquez, C. A nonlinear bilaplacian equation with hinged boundary conditions and very weak solutions: analysis and numerical solution. RACSAM 108, 867–879 (2014). https://doi.org/10.1007/s13398-013-0148-0

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  • DOI: https://doi.org/10.1007/s13398-013-0148-0

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