The boundary stabilization problem of a Timoshenko beam attached with a mass at one end is studied. First, with linear boundary force feedback and moment control simultaneously at the end attached with the load, the e...The boundary stabilization problem of a Timoshenko beam attached with a mass at one end is studied. First, with linear boundary force feedback and moment control simultaneously at the end attached with the load, the energy corresponding to the closed loop system is proven to be exponentially convergent to zero as time t →∞. Then, some counterexamples are given to show that, in other casest the corresponding closed loop system is, in general, not stable asymtotically, let alone exponentially.展开更多
A wave equation with variable coefficients and nonlinear boundary feedback is studied. The results of energy decay of the solution are obtained by multiplier method and Riemann geometry method. Previous results obtain...A wave equation with variable coefficients and nonlinear boundary feedback is studied. The results of energy decay of the solution are obtained by multiplier method and Riemann geometry method. Previous results obtained in the literatures are generalized in this paper.展开更多
基金Project supported by the the National Key Project of China.
文摘The boundary stabilization problem of a Timoshenko beam attached with a mass at one end is studied. First, with linear boundary force feedback and moment control simultaneously at the end attached with the load, the energy corresponding to the closed loop system is proven to be exponentially convergent to zero as time t →∞. Then, some counterexamples are given to show that, in other casest the corresponding closed loop system is, in general, not stable asymtotically, let alone exponentially.
基金This research is supported by the National Science Foundation of China under Grant No. 60774014 and the Science Foundation of Shanxi Province under Grant No. 2007011002. The authors would like to express their sincere thanks to Shugen CHAI for his valuable comments and useful suggestions on the manuscript of this work.
文摘A wave equation with variable coefficients and nonlinear boundary feedback is studied. The results of energy decay of the solution are obtained by multiplier method and Riemann geometry method. Previous results obtained in the literatures are generalized in this paper.
