University of the Philippines Diliman
Diliman, Quezon City, Philippines
email: bituin@math.upd.edu.ph
Université de Rouen Normandie
Laboratoire de Mathématiques Raphaël Salem
France
email: Patrizia.Donato@univ-rouen.fr
Bituin Cabarrubias, Patrizia Donato
Abstract:
This article concerns the asymptotic behavior of the wave and heat equations
in periodically perforated domains with small holes and Dirichlet conditions
on the boundary of the holes. In the first part we extend to time-dependent
functions the periodic unfolding method for domains with small holes
introduced in [6]. Therein, the method was applied to the study of
elliptic problems with oscillating coefficients in domains with small holes,
recovering the homogenization result with a "strange term" originally obtained
in [11] for the Laplacian. In the second part we obtain some
homogenization results for the wave and heat equations with
oscillating coefficients in domains with small holes.
The results concerning the wave equation extend those obtained in [12]
for the case where the elliptic part of the operator is the Laplacian.
Submitted March 2, 2016. Published July 4, 2016.
Math Subject Classifications: 35B27, 35L20, 35K20.
Key Words: Periodic unfolding method; homogenization in perforated domains;
small holes; wave equation; heat equation.
Show me the PDF file (391 KB), TEX file for this article.
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Bituin Cabarrubias University of the Philippines Diliman Diliman, Quezon City, Philippines email: bituin@math.upd.edu.ph |
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Patrizia Donato Université de Rouen Normandie Laboratoire de Mathématiques Raphaël Salem France email: Patrizia.Donato@univ-rouen.fr |
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