Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 85, pp. 1-37.

Title: Periodic unfolding method for domains with very small inclusions
       
Authors: Jake Avila (Univ. of the Philippines Diliman, Quezon City, Philippines)
         Bituin Cabarrubias (Univ. of the Philippines Diliman, Quezon City, Philippines)

Abstract:
This work  creates a version of the periodic unfolding method suitable
for domains with very small inclusions in $R^N$ 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.