Stability for nonlinear wave motions damped by time-dependent frictions

Zhe Jiao, Yong Xu, Lijing Zhao

Abstract: Highlights•Our wave system models the nonlinear vibrations damped by time-varying frictions, subject to nonconvex force potential.•We solve the open problem which condition is optimal on the damping coefficient for the convergence for the system.•The major contribution is to present an effective method to prove the convergence for the system without the technical assumption (I-4).•Our results show whether the convergence is exponential or polynomial depends on the Lojasiewicz exponents.•We present some numerical simulations to illustrate the theoretical result.