Volume 29, 2023
|Number of page(s)||29|
|Published online||09 August 2023|
Controllability of surface gravity waves and the sloshing problem
ICMAT-CSIC, C/Nicolás Cabrera, no. 13-15 Campus de Cantoblanco, UAM, 28049 Madrid, Spain
2 Universidad Industrial de Santander, Escuela de Matemáticas, A.A. 678, Bucaramanga, Colombia
* Corresponding author: firstname.lastname@example.org
Accepted: 22 May 2023
We study the problem of controlling the free surface for a two dimensional solid container in the context of the gravity waves and the sloshing problem. By using conformal maps and the Dirichlet–Neumann operator, the problem is formulated as a second order evolutionary equation on the free surface involving a self-adjoint operator. We present then the appropriate Sobolev spaces where having solutions for the system and study the exact controllability through an observability inequality for the adjoint problem.
Mathematics Subject Classification: 35Q31 / 35J57 / 44A15
Key words: Controllability / gravity waves / the sloshing problem / Hilbert transform
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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