Uniform Stability of Damped Nonlinear Vibrations of an Elastic String

[摘要] Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov functional for the system.

[学科分类] 数学（综合）

[关键词] Uniform stability;Kirchoff type wave equation;Lyapunov functional;exponential energy decay.