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
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
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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