Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Multiscale homogenization of a class of nonlinear equations with applications in lubrication theory and applications
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.ORCID iD: 0000-0001-7029-1112
Department of Mathematics and Statistics, University of Cape Coast.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0001-8211-3671
2011 (English)In: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965, Vol. 9, no 1, p. 17-40Article in journal (Refereed) Published
Abstract [en]

We prove a homogenization result for monotone operators by using the method of multiscale convergence. More precisely, we study the asymptotic behavior as epsilon -> 0 of the solutions u(epsilon) of the nonlinear equation div a(epsilon)(x, del u(epsilon)) = div b(epsilon), where both a(epsilon) and b(epsilon) oscillate rapidly on several microscopic scales and a(epsilon) satisfies certain continuity, monotonicity and boundedness conditions. This kind of problem has applications in hydrodynamic thin film lubrication where the bounding surfaces have roughness on several length scales. The homogenization result is obtained by extending the multiscale convergence method to the setting of Sobolev spaces W-0(1,p)(Omega), where 1 < p < infinity. In particular we give new proofs of some fundamental theorems concerning this convergence that were first obtained by Allaire and Briane for the case p = 2.

Place, publisher, year, edition, pages
2011. Vol. 9, no 1, p. 17-40
National Category
Tribology (Interacting Surfaces including Friction, Lubrication and Wear) Mathematical Analysis
Research subject
Machine Elements; Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-4572Local ID: 2891d109-fb9a-4616-8ee7-ecbb11c4cc2cOAI: oai:DiVA.org:ltu-4572DiVA: diva2:977446
Note
Validerad; 2011; 20110318 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-01-10Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

http://www.jfsa.net/

Search in DiVA

By author/editor
Almqvist, AndreasEssel, Emmanuel KwameFabricius, JohnWall, Peter
By organisation
Machine ElementsMathematical Science
In the same journal
Journal of Function Spaces and Applications
Tribology (Interacting Surfaces including Friction, Lubrication and Wear)Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 57 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf