Homogenization of some evolution problems in domains with small holes
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/169/abstr.html |
| _version_ | 1811193528917688320 |
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| author | Bituin Cabarrubias Patrizia Donato |
| author_facet | Bituin Cabarrubias Patrizia Donato |
| author_sort | Bituin Cabarrubias |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T00:10:04Z |
| format | Article |
| id | doaj.art-0a5a5bb6f649432988e38c31ded34f56 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T00:10:04Z |
| publishDate | 2016-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-0a5a5bb6f649432988e38c31ded34f562022-12-22T03:55:58ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912016-07-012016169,126Homogenization of some evolution problems in domains with small holesBituin Cabarrubias0Patrizia Donato1 Univ. of the Philippines, Diliman, Philippines Univ. de Rouen Normandie, France 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.http://ejde.math.txstate.edu/Volumes/2016/169/abstr.htmlPeriodic unfolding methodhomogenization in perforated domainssmall holeswave equationheat equation |
| spellingShingle | Bituin Cabarrubias Patrizia Donato Homogenization of some evolution problems in domains with small holes Electronic Journal of Differential Equations Periodic unfolding method homogenization in perforated domains small holes wave equation heat equation |
| title | Homogenization of some evolution problems in domains with small holes |
| title_full | Homogenization of some evolution problems in domains with small holes |
| title_fullStr | Homogenization of some evolution problems in domains with small holes |
| title_full_unstemmed | Homogenization of some evolution problems in domains with small holes |
| title_short | Homogenization of some evolution problems in domains with small holes |
| title_sort | homogenization of some evolution problems in domains with small holes |
| topic | Periodic unfolding method homogenization in perforated domains small holes wave equation heat equation |
| url | http://ejde.math.txstate.edu/Volumes/2016/169/abstr.html |
| work_keys_str_mv | AT bituincabarrubias homogenizationofsomeevolutionproblemsindomainswithsmallholes AT patriziadonato homogenizationofsomeevolutionproblemsindomainswithsmallholes |