Global solvability and uniform decays of solutions to quasilinear 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) × L2(Ω) norms of the initial data arc sufficiently small. The result presented in this paper extends/generalizes 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.

Publication Title

Communications in Partial Differential Equations