Jake Avila, Bituin Cabarrubias
Abstract:
This work creates a version of the periodic unfolding method suitable
for domains with very small inclusions in \(\mathbb{R}^N\) for \(N\geq 3\).
In the first part, we explore the properties of the associated operators.
The second part involves the application of the method in obtaining the asymptotic
behavior of a stationary heat dissipation problem depending on the parameter
\( \gamma < 0\). In particular, we consider the cases when \(\gamma \in (-1,0)\),
\( \gamma < -1\) and \(\gamma = -1\). We also include here the corresponding corrector
results for the solution of the problem, to complete the homogenization process.
Submitted September 13, 2023. Published December 20, 2023.
Math Subject Classifications: 35B27, 35M32, 35Q79.
Key Words: Homogenization; imperfect interface; small inclusions; unfolding method.
DOI: 10.58997/ejde.2023.85
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Jake Avila Institute of Mathematics University of the Philippines Diliman 1101 Diliman, Quezon City, Philippines email: javila@math.upd.edu.ph |
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Bituin Cabarrubias Institute of Mathematics University of the Philippines Diliman 1101 Diliman, Quezon City, Philippines email: bituin@math.upd.edu.ph |
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