A NOTE ON THE CONTROL AND STABILIZATION OF A HIGHER-ORDER WATER WAVE MODEL

Bautista G.; Pazoto A. · Discrete and Continuous Dynamical Systems - Series B (2023) · DOI: 10.3934/dcdsb.2022133

Resumen

The paper deals with the internal controllability and stabilizability of a family of Boussinesq systems introduced by J. L. Bona, M. Chen and J.-C. Saut to describe two-way propagation of small amplitude gravity waves on the surface of water in a canal. By applying the moment method, we first obtain the exact controllability of the linearized system in suitable Hilbert spaces, which implies its exponential stabilization by suitable feedback. Then, by using a contraction mapping principle, we establish the local exact controllability and exponential stabilization for the original nonlinear system.

Instituciones: Universidad Tecnológica de los Andes