2019/04/06 by Mahendra Panthee, Panthee, M., Francisco J. Vielma Leal +1
Engineering · Mathematics · #35Q53 #93B05 #93D15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1904.03492
openalex publication_date 2019/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to study the controllability and stabilization for the Benjamin equation on a periodic domain \mathbbT. We show that the Benjamin equation is globally exactly controllable and globally exponentially stabilizable in Hps(\mathbbT), with s≥ 0. First we prove propagation of compactness, propagation of regularity of solution in Bourgain's spaces and unique continuation property, and use them to obtain the global exponential stabilizability corresponding to a natural feedback law. Combining the global exponential stability and the local controllability result we prove the global controllability as well. Also, we prove that the closed-loop system with a different feedback control law is locally exponentially stable with an arbitrary decay rate. Finally, a time-varying feedback law is designed to guarantee a global exponential stability with an arbitrary decay rate. The results obtained here extend the ones we proved for the linearized Benjamin equation in \citeVielma and Panthee.