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A note on the exact boundary controllability for an imperfect transmission problem

Monsurro, S and Nandakumaran, AK and Perugia, C (2021) A note on the exact boundary controllability for an imperfect transmission problem. In: Ricerche di Matematica .

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Official URL: https://doi.org/10.1007/s11587-021-00625-w


In this note, we consider a hyperbolic system of equations in a domain made up of two components. We prescribe a homogeneous Dirichlet condition on the exterior boundary and a jump of the displacement proportional to the conormal derivatives on the interface. This last condition is the mathematical interpretation of an imperfect interface. We apply a control on the external boundary and, by means of the Hilbert Uniqueness Method, introduced by J. L. Lions, we study the related boundary exact controllability problem. The key point is to derive an observability inequality by using the so called Lagrange multipliers method, and then to construct the exact control through the solution of an adjoint problem. Eventually, we prove a lower bound for the control time which depends on the geometry of the domain, on the coefficients matrix and on the proportionality between the jump of the solution and the conormal derivatives on the interface.

Item Type: Journal Article
Publication: Ricerche di Matematica
Publisher: Springer-Verlag Italia s.r.l.
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Exact controllability; HUM; Imperfect interface condition; Second order hyperbolic equations
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 06 Jun 2023 10:11
Last Modified: 06 Jun 2023 10:11
URI: https://eprints.iisc.ac.in/id/eprint/81822

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