Homogenization with strong contrasting diffusivity in a circular oscillating domain with L1 source term

Nandakumaran, AK and Sufian, A and Thazhathethil, R (2022) Homogenization with strong contrasting diffusivity in a circular oscillating domain with L1 source term. In: Annali di Matematica Pura ed Applicata .

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Abstract

In this article, we study the homogenization of an elliptic variational form with oscillating coefficients in a circular, highly oscillating domain, where the oscillatory part is made of two materials with high contrasting conductivity (or diffusivity) with the source term in L1. We incorporate this phenomenon, namely, highly oscillating boundary, rapid oscillating coefficient, and the oscillating part made of high contrasting materials, which leads to non-uniform ellipticity as the oscillating parameter goes to 0. Further, due to the L1 source term, the solutions are interpreted as renormalized solutions. To achieve our primary goal, we have proved the strong convergence results in the context of the L2 source term in the first part (corrector results). In the second part, we have homogenized the renormalized variational form and established the relation between the ε-stage renormalized solution and the limit renormalized solution via convergence results. The unfolding operator for the polar coordinates is a central tool for the analysis. © 2022, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature.

Item Type:	Journal Article
Publication:	Annali di Matematica Pura ed Applicata
Publisher:	Institute for Ionics
Additional Information:	The copyright for this article belongs to the Institute for Ionics.
Keywords:	Circular oscillating domain; Homogenization; Oscillating boundary domain; Periodic unfolding; Renormalized solution
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	06 Oct 2022 11:16
Last Modified:	06 Oct 2022 11:16
URI:	https://eprints.iisc.ac.in/id/eprint/77262

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