Homogenization of a quasilinear problem with semilinear terms in a two-component domain

Abstract

This paper deals with the asymptotic behavior of a quasilinear elliptic problem with semilinear terms situated in a two-component domain in ${\mathbb{R}}^N$, $N\ge 2$, as ε approaches 0. The domain has an $ϵ-$periodic interface where the flux is discontinuous and the temperature field, depending on the real parameter $\gamma <1$, is proportional to the flux. We use the Periodic Unfolding Method for two-component domains to obtain the homogenized property of the problem separating the cases $\gamma \in (-1,1)$, $\gamma <-1$ and $\gamma =-1$. The corrector results are also presented, lastly, which completes the whole homogenization process.

Keywords:

• Homogenization
• periodic unfolding method
• quasilinear problem
• semilinear terms
• two-component domains

Mathematics Subject Classifications (2000):

• 35B27
• 35J62
• 35M32

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 A copy can be requested from the second author.

2 A copy can be requested from the second author.

Additional information

Funding

The authors would like to extend their gratitude to the Department of Science and Technology (DOST) through the Accelerated Science and Technology Human Resource Development Program-National Science Consortium (ASTHRDP-NSC) (first author) and the University of the Philippines System Enhanced Creative Work and Research Grant (ECWRG 2019-04-R) (second author) for funding this work.