Volume 27, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Number of page(s)||37|
|Published online||01 March 2021|
Oscillating PDE in a rough domain with a curved interface: Homogenization of an Optimal Control Problem
Department of Mathematics, Indian Institute of Science,
* Corresponding author: firstname.lastname@example.org
Accepted: 13 July 2020
Homogenization of an elliptic PDE with periodic oscillating coefficients and associated optimal control problems with energy type cost functional is considered. The domain is a 3-dimensional region (method applies to any n dimensional region) with oscillating boundary, where the base of the oscillation is curved and it is given by a Lipschitz function. Further, we consider general elliptic PDE with oscillating coefficients. We also include very general type functional of Dirichlet type given with oscillating coefficients which can be different from the coefficient matrix of the equation. We introduce appropriate unfolding operators and approximate unfolded domain to study the limiting analysis. The present article is new in this generality.
Mathematics Subject Classification: 49J20 / 80M35 / 35B27
Key words: Optimal control / asymptotic analysis / unfolding operator / oscillating boundary / Homogenization
© EDP Sciences, SMAI 2021
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