LONG-TIME ASYMPTOTICS OF A LINEAR HIGHER-ORDER WATER WAVE MODEL

Bautista G.J.; Sierra Fonseca O.A. · Communications on Pure and Applied Analysis (2023) · DOI: 10.3934/cpaa.2023121

Resumen

We consider higher-order Benjamin-Bona-Mahony-type equations with damping mechanisms, focusing on internal and boundary stabilization of the associated linear model. This work extends existing results from the lower-order case and coupled Boussinesq systems, describing the asymptotic behavior of solutions. Initially, we study the higher-order Benjamin-Bona-Mahony-type equation with various damping mechanisms, demonstrating energy decay rates in both internal and boundary-damping cases. Finally, once the result of the unique continuation property is proved, we show the convergence of solutions towards zero or the mean of the initial datum under specific conditions.

Instituciones: Universidad Tecnológica de los Andes