- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 329704, 6 pages
A Note on Parabolic Homogenization with a Mismatch between the Spatial Scales
Department of Quality Technology and Management, Mechanical Engineering and Mathematics, Mid Sweden University,
83125 Östersund, Sweden
Received 16 May 2013; Accepted 29 August 2013
Academic Editor: Rodrigo Lopez Pouso
Copyright © 2013 Liselott Flodén et al. 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.
- G. Allaire and M. Briane, “Multiscale convergence and reiterated homogenisation,” Proceedings of the Royal Society of Edinburgh A, vol. 126, no. 2, pp. 297–342, 1996.
- L. Flodén, A. Holmbom, M. Olsson, and J. Persson, “Very weak multiscale convergence,” Applied Mathematics Letters, vol. 23, no. 10, pp. 1170–1173, 2010.
- J. L. Woukeng, “Periodic homogenization of nonlinear non-monotone parabolic operators with three time scales,” Annali di Matematica Pura ed Applicata, vol. 189, no. 3, pp. 357–379, 2010.
- L. Flodén and M. Olsson, “Homogenization of some parabolic operators with several time scales,” Applications of Mathematics, vol. 52, no. 5, pp. 431–446, 2007.
- A. Holmbom, “Homogenization of parabolic equations: an alternative approach and some corrector-type results,” Applications of Mathematics, vol. 42, no. 5, pp. 321–343, 1997.
- G. Nguetseng and J. L. Woukeng, “-convergence of nonlinear parabolic operators,” Nonlinear Analysis. Theory, Methods & Applications, vol. 66, no. 4, pp. 968–1004, 2007.
- J. L. Woukeng, “-convergence and reiterated homogenization of nonlinear parabolic operators,” Communications on Pure and Applied Analysis, vol. 9, no. 6, pp. 1753–1789, 2010.
- L. Flodén, A. Holmbom, M. O. Lindberg, and J. Persson, “Detection of scales of heterogeneity and parabolic homogenization applying very weak multiscale convergence,” Annals of Functional Analysis, vol. 2, no. 1, pp. 84–99, 2011.
- A. Bensoussan, J.-L. Lions, and G. Papanicolaou, Asymptotic analysis for periodic structures, vol. 5 of Studies in Mathematics and its Applications, North-Holland Publishing Co., Amsterdam, The Netherlands, 1978.
- A. Piatnitski, “A parabolic equation with rapidly oscillating coefficients,” Moscow University Mathematics Bulletin, vol. 35, no. 3, pp. 35–42, 1980.
- J. Garnier, “Homogenization in a periodic and time-dependent potential,” SIAM Journal on Applied Mathematics, vol. 57, no. 1, pp. 95–111, 1997.
- A. K. Nandakumaran and M. Rajesh, “Homogenization of a nonlinear degenerate parabolic differential equation,” Electronic Journal of Differential Equations, vol. 2001, no. 17, pp. 1–19, 2001.
- N. Svanstedt and J. L. Woukeng, “Periodic homogenization of strongly nonlinear reaction-diffusion equations with large reaction terms,” Applicable Analysis, vol. 92, no. 7, pp. 1–22, 2012.
- L. Flodén, A. Holmbom, and M. Olsson Lindberg, “A strange term in the homogenization of parabolic equations with two spatial and two temporal scales,” Journal of Function Spaces and Applications, vol. 2012, Article ID 643458, 9 pages, 2012.
- G. Nguetseng, “A general convergence result for a functional related to the theory of homogenization,” SIAM Journal on Mathematical Analysis, vol. 20, no. 3, pp. 608–623, 1989.
- G. Allaire, “Homogenization and two-scale convergence,” SIAM Journal on Mathematical Analysis, vol. 23, no. 6, pp. 1482–1518, 1992.
- J. Persson, Selected topics in homogenization [Doctoral thesis], Mid Sweden University, Östersund, Sweden, 2012.
- E. Zeidler, Nonlinear Functional Analysis and Its Applications, Springer, New York, NY, USA, 1990.
- S. Spagnolo, “Convergence of parabolic equations,” Bollettino della Unione Matematica Italiana. Serie VIII. Sezione B, vol. 14, no. 2, pp. 547–568, 1977.
- N. Svanstedt, G-convergence and homogenization of sequences of linear and nonlinear partial differential operators [Doctoral thesis], Department of Mathematics, Luleå University of Technology, Luleå, Sweden, 1992.
- F. Paronetto, “-convergence of mixed type evolution operators,” Journal de Mathématiques Pures et Appliquées, vol. 93, no. 4, pp. 361–407, 2010.
- L. E. Persson, L. Persson, N. Svanstedt, and J. Wyller, The homogenization Method. An Introduction, Studentlitteratur, Lund, Sweden, Chartwell-Bratt, Bromley, UK, 1993.