Stabilization of wave equation with variable coefficients by nonlinear boundary feedback

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.

[1]  Peng-Fei Yao Observability Inequalities for Shallow Shells , 2000, SIAM J. Control. Optim..

[2]  AISSA GUESMIA,et al.  A New Approach of Stabilization of Nondissipative Distributed Systems , 2003, SIAM J. Control. Optim..

[3]  J. Lions Exact controllability, stabilization and perturbations for distributed systems , 1988 .

[4]  V. Komornik Exact Controllability and Stabilization: The Multiplier Method , 1995 .

[5]  Ilhem Hamchi,et al.  Uniform decay rates for second-order hyperbolic equations with variable coefficients , 2008, Asymptot. Anal..

[6]  Graham H. Williams,et al.  Exact controllability for problems of transmission of the plate equation with lower-order terms , 2000 .

[7]  Peng-Fei Yao,et al.  On The Observability Inequalities for Exact Controllability of Wave Equations With Variable Coefficients , 1999 .

[8]  Dexing Feng,et al.  Nonlinear Internal Damping of Wave Equations with Variable Coefficients , 2004 .

[9]  Irena Lasiecka,et al.  Inverse/Observability Estimates for Second-Order Hyperbolic Equations with Variable Coefficients , 1999 .

[10]  Weijiu Liu,et al.  Stabilization and controllability for the transmission wave equation , 2001, IEEE Trans. Autom. Control..

[11]  A. Wyler Stability of wave equations with dissipative boundary conditions in a bounded domain , 1994, Differential and Integral Equations.

[12]  Dexing Feng,et al.  Boundary stabilization of wave equations with variable coefficients , 2001 .

[13]  Shugen Chai,et al.  Boundary Feedback Stabilization of Shallow Shells , 2003, SIAM J. Control. Optim..