ON UNIFORM STABILIZATION OF A SEMILINEAR WAVE EQUATION WITH VARIABLE COEFFICIENTS UNDER THE NONLINEAR BOUNDARY FEEDBACK1

The uniform stabilization of a nondissipative system described by a semilinear wave equation with variable coefficients under the nonlinear boundary feedback is considered. The existence of both weak and strong solutions to the system is proved by Galerkin method. The exponential stability of the system is obtained by the Riemannian geometry method. The result generalizes that for the wave equation with constant coefficients.