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Exact controllability in fluid–solid structure : the Helmholtz model

Jean-Pierre Raymond, Muthusamy Vanninathan (2005)

ESAIM: Control, Optimisation and Calculus of Variations

A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability results....

Exact controllability of the 1-d wave equation from a moving interior point

Carlos Castro (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the linear wave equation with Dirichlet boundary conditions in a bounded interval, and with a control acting on a moving point. We give sufficient conditions on the trajectory of the control in order to have the exact controllability property.

Existence and stability results of nonlinear higher-order wave equation with a nonlinear source term and a delay term

Mama Abdelli, Abderrahmane Beniani, Nadia Mezouar, Ahmed Chahtou (2023)

Mathematica Bohemica

We consider the initial-boundary value problem for a nonlinear higher-order nonlinear hyperbolic equation in a bounded domain. The existence of global weak solutions for this problem is established by using the potential well theory combined with Faedo-Galarkin method. We also established the asymptotic behavior of global solutions as t → ∞ by applying the Lyapunov method.

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