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Optimal control problem in a domain with branched structure and homogenization

Aiyappan, S and Nandakumaran, A K (2017) Optimal control problem in a domain with branched structure and homogenization. In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 40 (8). pp. 3173-3189.

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Official URL: http://dx.doi.org/10.1002/mma.4231

Abstract

We consider a linear parabolic problem in a thick junction domain which is the union of a fixed domain and a collection of periodic branched trees of height of order 1 and small width connected on a part of the boundary. We consider a three-branched structure, but the analysis can be extended to n-branched structures. We use unfolding operator to study the asymptotic behavior of the solution of the problem. In the limit problem, we get a multi-sheeted function in which each sheet is the limit of restriction of the solution to various branches of the domain. Homogenization of an optimal control problem posed on the above setting is also investigated. One of the novelty of the paper is the characterization of the optimal control via the appropriately defined unfolding operators. Finally, we obtain the limit of the optimal control problem. Copyright (c) 2016 John Wiley & Sons, Ltd.

Item Type: Journal Article
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Additional Information: Copy right for this article belongs to the WILEY, 111 RIVER ST, HOBOKEN 07030-5774, NJ USA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 10 Jun 2017 04:38
Last Modified: 10 Jun 2017 04:38
URI: http://eprints.iisc.ernet.in/id/eprint/57151

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