Control and Stabilization of the Rosenau Equation Posed on a Periodic Domain

摘要

This paper considers the Rosenau equation with a moving control (a)tu+(a)t(a)4xu+(a)xu+u(a)xu=a(x+ct)h(x,t),c≠0,x∈T=R/(2πZ),t＞0.The authors prove that the Rosenau equation with a moving control is locally exact controllable in Hs(T) with s ≥ 0 and globally exponential stable in Hs(T) with s ≥ 2.The two results nontrivially extend the work of (Rosier L and Zhang B Y,2013) from the BBM equation to the Rosenau equation.