Monsurro, S and Nandakumaran, AK and Perugia, C (2022) Exact Internal Controllability for a Problem with Imperfect Interface. In: Applied Mathematics and Optimization .
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Abstract
In this paper, we study the internal exact controllability for a second order linear evolution equation defined in a two-component domain. On the interface, we prescribe a jump of the solution proportional to the conormal derivatives, meanwhile a homogeneous Dirichlet condition is imposed on the exterior boundary. Due to the geometry of the domain, we apply controls through two regions which are neighborhoods of a part of the external boundary and of the whole interface, respectively. Our approach to internal exact controllability consists in proving an observability inequality by using the Lagrange multipliers method. Eventually, we apply the Hilbert Uniqueness Method, introduced by Lions, which leads to the construction of the exact control through the solution of an adjoint problem. Finally, we find a lower bound for the control time depending not only on the geometry of our domain and on the matrix of coefficients of our problem but also on the coefficient of proportionality of the jump with respect to the conormal derivatives. © 2022, The Author(s).
| Item Type: | Journal Article |
|---|---|
| Publication: | Applied Mathematics and Optimization |
| Publisher: | Springer |
| Additional Information: | The copyright for this article belongs to the author. |
| Keywords: | Lagrange multipliers; Observability, Dirichlet condition; Exact controllability; HUM; Imperfect interface; Imperfect interface condition; Interface conditions; Linear evolution equations; Second orders; Second-order hyperbolic equations; Two-component, Controllability |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 27 May 2022 05:56 |
| Last Modified: | 27 May 2022 05:56 |
| URI: | https://eprints.iisc.ac.in/id/eprint/72753 |
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