104 research outputs found
Internal controllability of the Korteweg-de Vries equation on a bounded domain
This paper is concerned with the control properties of the Korteweg-de Vries
(KdV) equation posed on a bounded interval with a distributed control. When the
control region is an arbitrary open subdomain, we prove the null
controllability of the KdV equation by means of a new Carleman inequality. As a
consequence, we obtain a regional controllability result, the state function
being controlled on the left part of the complement of the control region.
Finally, when the control region is a neighborhood of the right endpoint, an
exact controllability result in a weighted L2 space is also established
Generation of two-dimensional water waves by moving bottom disturbances
We investigate the potential and limitations of the wave generation by
disturbances moving at the bottom. More precisely, we assume that the wavemaker
is composed of an underwater object of a given shape which can be displaced
according to a prescribed trajectory. We address the practical question of
computing the wavemaker shape and trajectory generating a wave with prescribed
characteristics. For the sake of simplicity we model the hydrodynamics by a
generalized forced Benjamin-Bona-Mahony (BBM) equation. This practical problem
is reformulated as a constrained nonlinear optimization problem. Additional
constraints are imposed in order to fulfill various practical design
requirements. Finally, we present some numerical results in order to
demonstrate the feasibility and performance of the proposed methodology.Comment: 21 pages, 7 figures, 1 table, 69 references. Other author's papers
can be downloaded at http://www.denys-dutykh.com
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