A NEW METHOD TO OBTAIN UNIFORM DECAY RATES FOR MULTIDIMENSIONAL WAVE EQUATIONS WITH NONLINEAR ACOUSTIC BOUNDARY CONDITIONS

摘要

In this paper, we investigate the uniform stability of a class of nonlinear acoustic wave motions with boundary and localized interior damping. Here the damping and potential in the boundary displacement equation are nonlinear. Moreover, the nonlinear system contains the localized interior damping term, which indicates that there is a thin absorption material and flow resistance on the endophragm of the boundary. Since some lower-order term in the nonlinear wave system is not below the energy level, the "compactness-uniqueness" method is not suitable for the problem. Our main purpose is to present a new method to obtain uniform decay rates for these damped wave equations with nonlinear acoustic boundary conditions.