Global existence and stability for semilinear wave equations damped by time-dependent boundary frictions

摘要

Semilinear wave equations with time-dependent boundary dampings are considered. We prove global existence of the solution, and establish uniform decay rates of the energy of the non-autonomous system. From the results, one can see that the growth conditions of the damping term determine the form of the energy decay, polynomial or exponential decay, and the coefficient of the damping influences the speed of the energy decay. To the best of our knowledge, there has been few work about the well-posedness and decay rates of a multi-dimensional wave equation with a time-dependent boundary dissipation.