Adaptive stabilization of the sine-Gordon equation by boundary control

摘要

This paper is concerned with adaptive global stabilization of the sine-Gordon equation without damping by boundary control. An adaptive stabilizer is constructed by the concept of high-gain output feedback. The closed-loop system is shown to be locally well-posed by the Banach fixed point theorem and then to be globally well-posed by the Lyapunov method. Moreover, using a multiplier method global exponential stabilization of the system is proved. Copyright (C) 2004 John Wiley Sons, Ltd.