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Multiscale homogenization of a class of nonlinear equations with applications in lubrication theory and applications
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.ORCID-id: 0000-0001-7029-1112
Department of Mathematics and Statistics, University of Cape Coast.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.ORCID-id: 0000-0003-1993-8229
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.ORCID-id: 0000-0001-8211-3671
2011 (engelsk)Inngår i: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965, Vol. 9, nr 1, s. 17-40Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
2011. Vol. 9, nr 1, s. 17-40
HSV kategori
Forskningsprogram
Maskinelement; Matematik
Identifikatorer
URN: urn:nbn:se:ltu:diva-4572Lokal ID: 2891d109-fb9a-4616-8ee7-ecbb11c4cc2cOAI: oai:DiVA.org:ltu-4572DiVA, id: diva2:977446
Merknad
Validerad; 2011; 20110318 (andbra)Tilgjengelig fra: 2016-09-29 Laget: 2016-09-29 Sist oppdatert: 2018-03-08bibliografisk kontrollert

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