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.
Keywords: Optimal control, asymptotic analysis, unfolding operator, oscillating boundary, Homogenization
@article{COCV_2021__27_S1_A5_0,
author = {Nandakumaran, A. K. and Sufian, Abu},
title = {Oscillating {PDE} in a rough domain with a curved interface: {Homogenization} of an {Optimal} {Control} {Problem}},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2020045},
mrnumber = {4222166},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2020045/}
}
TY - JOUR AU - Nandakumaran, A. K. AU - Sufian, Abu TI - Oscillating PDE in a rough domain with a curved interface: Homogenization of an Optimal Control Problem JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2020045/ DO - 10.1051/cocv/2020045 LA - en ID - COCV_2021__27_S1_A5_0 ER -
%0 Journal Article %A Nandakumaran, A. K. %A Sufian, Abu %T Oscillating PDE in a rough domain with a curved interface: Homogenization of an Optimal Control Problem %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2020045/ %R 10.1051/cocv/2020045 %G en %F COCV_2021__27_S1_A5_0
Nandakumaran, A. K.; Sufian, Abu. Oscillating PDE in a rough domain with a curved interface: Homogenization of an Optimal Control Problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. S4. doi: 10.1051/cocv/2020045
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