Global solvability and uniform decays of solutions to quaslinear equation with nonlinear boundary dissipation

A n-dimensional quasiliner wave equation with nonlinear boundary dissipation is considered. Global existence, uniqueness and uniform decay rates are established for the model, under the assumption that the H¹(Ω)xL₂(Ω') norms of the initial data are sufficiently small. The result presented in this paper extends/generalizes those obtained those obtained recently in (13), where, by contrast, interior nonlinear damping was considered; and those obtained in (31), where the one-dimensional wave equation with linear boundary damping was treated.