Abstract
This chapter is devoted to the homogenization of boundary value problems in a periodically perforated domain by an approach which is alternative to those of asymptotic analysis and of classical homogenization theory. The domain has a periodic structure, and the size of each cell is determined by a positive parameter δ. The relative size of each periodic perforation is instead determined by a positive parameter ε. We analyze the behavior of a family of solutions as δ and ε degenerate to zero.
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Acknowledgements
The authors acknowledge the support of “Progetto di Ateneo: Singular perturbation problems for differential operators, CPDA120171/12,” University of Padova, and of Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).
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de Cristoforis, M.L., Musolino, P. (2015). A Functional Analytic Approach to Homogenization Problems. In: Constanda, C., Kirsch, A. (eds) Integral Methods in Science and Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-16727-5_30
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DOI: https://doi.org/10.1007/978-3-319-16727-5_30
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-16726-8
Online ISBN: 978-3-319-16727-5
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