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

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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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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Keywords

  • Very weak solutions
  • Distance to the boundary
  • Nonlinear bilaplacian operator
  • Hinged boundary conditions
  • Numerical methods
  • Finite elements

Mathematics Subject Classification

  • 35G50
  • 35G60
  • 74G25
  • 74G15