Electron. J. Differential Equations,
Vol. 2017 (2017), No. 186, pp. 1-24.
Approximate controllability of a semilinear elliptic problem with Robin
condition in a periodically perforated domain
Nikita Agarwal, Carlos Conca, Indira Mishra
Abstract:
In this article, we study the approximate controllability and homegenization
results of a semi-linear elliptic problem with Robin boundary condition in
a periodically perforated domain. We prove the existence of minimal norm
control using Lions constructive approach, which is based on
Fenchel-Rockafeller duality theory, and by means of Zuazua's fixed point
arguments. Then, as the homogenization parameter goes to zero, we link the
limit of the optimal controls (the limit of fixed point of the controllability
problems) with the optimal control of the corresponding homogenized problem.
Submitted February 4, 2017. Published July 23, 2017.
Math Subject Classifications: 35J15, 35B27, 35J57, 49J20.
Key Words: Approximate controllability; semilinear elliptic equation;
homogenization; periodic perforated domain;
Robin boundary condition.
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Nikita Agarwal
Indian Institute of Science Education and Research Bhopal
Bhopal Bypass Road, Bhauri,
Bhopal 462 066
Madhya Pradesh, India
email: nagarwal@iiserb.ac.in
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Carlos Conca
Department of Mathematical Engineering (DIM)
Center for Mathematical Modelling (CMM, UMI CNRS 2807)
Center for Biotechnology and Bioengineering (CeBiB)
University of Chile
Beaucheff 851, Santiago, Chile
email: cconca@dim.uchile.cl
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Indira Mishra
Indian Institute of Science Education and Research Bhopal
Bhopal Bypass Road, Bhauri,
Bhopal 462 066
Madhya Pradesh, India
email: indira.mishra1@gmail.com, indira@iiserb.ac.in
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