Journal Articles Journal of Differential Equations Year : 2013

Unique continuation property and control for the Benjamin-Bona-Mahony equation on the torus

Abstract

We consider the Benjamin-Bona-Mahony (BBM) equation on the one dimensional torus T = R/(2πZ). We prove a Unique Continuation Property (UCP) for small data in H^1(T) with nonnegative zero means. Next we extend the UCP to certain BBM-like equations, including the equal width wave equation and the KdV-BBM equation. Applications to the stabilization of the above equations are given. In particular, we show that when an internal control acting on a moving interval is applied in BBM equation, then a semiglobal exponential stabilization can be derived in H^s(T) for any s ≥ 1. Furthermore, we prove that the BBM equation with a moving control is also locally exactly controllable in H^s(T) for any s ≥ 0 and globally exactly controllable in H s (T) for any s ≥ 1.
Fichier principal
Vignette du fichier
BBM-subm.pdf (369) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-00669334 , version 1 (13-02-2012)

Identifiers

Cite

Lionel Rosier, Bing-Yu Zhang. Unique continuation property and control for the Benjamin-Bona-Mahony equation on the torus. Journal of Differential Equations, 2013, 254 (1), pp.141-178. ⟨10.1016/j.jde.2012.08.014⟩. ⟨hal-00669334⟩
132 View
273 Download

Altmetric

Share

More