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A note on parabolic homogenization with a mismatch between the spatial scales
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics. (Tillämpad matematik)ORCID iD: 0000-0001-6742-5781
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics. (Tillämpad matematik)ORCID iD: 0000-0003-2942-6841
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics. (Tillämpad matematik)ORCID iD: 0000-0001-9984-2424
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
2013 (English)In: Abstract and Applied Analysis, ISSN 1085-3375, E-ISSN 1687-0409, Art. no. 329704- p.Article in journal (Refereed) Published
Abstract [en]

We consider the homogenization of the linear parabolic problem rho(x/epsilon(2))partial derivative(t)u(epsilon)(x,t) - del . (a(x/epsilon(1), t/epsilon(2)(1))del u(epsilon) (x,t)) = f(x,t) which exhibits a mismatch between the spatial scales in the sense that the coefficient a(x/epsilon(1), t/epsilon(2)(1)) of the elliptic part has one frequency of fast spatial oscillations, whereas the coefficient rho(x/epsilon(2)) of the time derivative contains a faster spatial scale. It is shown that the faster spatialmicroscale does not give rise to any corrector termand that there is only one local problemneeded to characterize the homogenized problem. Hence, the problem is not of a reiterated type even though two rapid scales of spatial oscillation appear.

Place, publisher, year, edition, pages
Hindawi Publishing Corporation, 2013. Art. no. 329704- p.
Keyword [en]
Partial differential equations, parabolic, homogenization, two-scale convergence
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-20017DOI: 10.1155/2013/329704ISI: 000325558500001Scopus ID: 2-s2.0-84886475240OAI: oai:DiVA.org:miun-20017DiVA: diva2:657328
Available from: 2013-10-18 Created: 2013-10-18 Last updated: 2016-12-12Bibliographically approved

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Holmbom, AndersOlsson Lindberg, MariannePersson, JensFlodén, Liselott
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