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EXACT INTERNAL CONTROLLABILITY FOR THE WAVE EQUATION IN A DOMAIN WITH OSCILLATING BOUNDARY WITH NEUMANN BOUNDARY CONDITION

De Maio, Umberto and Nandakumaran, Akamabadath K and Perugia, Carmen (2015) EXACT INTERNAL CONTROLLABILITY FOR THE WAVE EQUATION IN A DOMAIN WITH OSCILLATING BOUNDARY WITH NEUMANN BOUNDARY CONDITION. In: EVOLUTION EQUATIONS AND CONTROL THEORY, 4 (3). pp. 325-346.

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Official URL: http://dx.doi.org/10.3934/eect.2015.4.325

Abstract

In this paper, we study the exact controllability of a second order linear evolution equation in a domain with highly oscillating boundary with homogeneous Neumann boundary condition on the oscillating part of boundary. Our aim is to obtain the exact controllability for the homogenized equation. The limit problem with Neumann condition on the oscillating boundary is different and hence we need to study the exact controllability of this new type of problem. In the process of homogenization, we also study the asymptotic analysis of evolution equation in two setups, namely solution by standard weak formulation and solution by transposition method.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the AMER INST MATHEMATICAL SCIENCES-AIMS, PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA
Keywords: Wave equation; homogenization; oscillating boundary; exact controllability
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 29 Feb 2016 07:13
Last Modified: 29 Feb 2016 07:13
URI: http://eprints.iisc.ac.in/id/eprint/53333

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