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

Abstract

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.