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Journal of Function Spaces and Applications
Volume 5, Issue 2, Pages 133-150
http://dx.doi.org/10.1155/2007/163670

Bounds on the effective behavior of a homogenized generalized Reynolds equation

1Dag Lukkassen and Annette Meidell, Narvik University College, P.O.B. 385 N-8505 Narvik, Norway
2Peter Wall, Department of Mathematics, Luleå University of Technology, SE-97187 Lulå, Sweden

Received 1 January 2006

Academic Editor: Björn Birnir

Copyright © 2007 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [12 citations]

The following is the list of published articles that have cited the current article.

  • Andreas Almqvist, John Fabricius, T. Staffan Lundström, and Peter Wall, “Flow in thin domains with a microstructure: Lubrication and thin porous media,” vol. 1798, pp. 020172, . View at Publisher · View at Google Scholar
  • Andreas Almqvist, Emmanuel Kwame Essel, John Fabricius, and Peter Wall, “Variational bounds applied to unstationary hydrodynamic lubrication,” International Journal of Engineering Science, vol. 46, no. 9, pp. 891–906, 2008. View at Publisher · View at Google Scholar
  • Dag Lukkassen, and Annette Meidell, “Effective properties of some new self-similar structures,” Applicable Analysis, vol. 87, no. 12, pp. 1297–1310, 2008. View at Publisher · View at Google Scholar
  • Dag Lukkassen, Annette Meidell, and Lars-Erik Persson, “Nonlinear Variational Methods for Estimating Effective Properties of Multiscale Materials,” Nonlinear Analysis and Variational Problems, vol. 35, pp. 367–414, 2009. View at Publisher · View at Google Scholar
  • Dag Lukkassen, Annette Meidell, and Peter Wall, “Homogenization of some variational problems connected to the theory of lubrication,” International Journal of Engineering Science, vol. 47, no. 1, pp. 153–162, 2009. View at Publisher · View at Google Scholar
  • Dag Lukkassen, Annette Meidell, and Peter Wall, “A New Approach for Estimating the Friction in Thin Film Lubrication,” Mathematical Problems In Engineering, 2010. View at Publisher · View at Google Scholar
  • Dag Lukkassen, Annette Meidell, and Peter Wall, “Homogenization of a Class of Nonlinear Variational Inequalities with Applications in Fluid Film Flow,” Chinese Annals Of Mathematics Series B, vol. 32, no. 3, pp. 417–434, 2011. View at Publisher · View at Google Scholar
  • Dag Lukkassen, Annette Meidell, and Peter Wall, “Analysis of the effects of rough surfaces in compressible thin film flow by homogenization,” International Journal of Engineering Science, vol. 49, no. 5, pp. 369–377, 2011. View at Publisher · View at Google Scholar
  • Andreas Almqvist, “Homogenization of the Reynolds Equation Governing Hydrodynamic Flow in a Rotating Device,” Journal of Tribology, vol. 133, no. 2, pp. 021705, 2011. View at Publisher · View at Google Scholar
  • Andreas Almqvist, John Fabricius, and Peter Wall, “Homogenization of a Reynolds equation describing compressible flow,” Journal of Mathematical Analysis and Applications, vol. 390, no. 2, pp. 456–471, 2012. View at Publisher · View at Google Scholar
  • M. Budt,  I. Temizer, and P. Wriggers, “A computational homogenization framework for soft elastohydrodynamic lubrication,” Computational Mechanics, vol. 49, no. 6, pp. 749–767, 2012. View at Publisher · View at Google Scholar
  • Dag Lukkassen, Annette Meidell, Peter Wall, Dag Lukkassen, Annette Meidell, and Peter Wall, “On the Role of Homogenization in Lubrication Theory The paper is dedicated to professor Lars-Erik Persson, on the occasion of his 70th birthday,” 10Th International Conference On Mathematical Problems In Engineering, Aerospace And Sciences (Icnpaa 2014), vol. 1637, pp. 1170–1176, 2014. View at Publisher · View at Google Scholar