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 , where, by contrast, interior nonlinear damping was considered; and those obtained in , where the one-dimensional wave equation with linear boundary damping was treated.
Communications in Partial Differential Equations
Lasiecka, I., & Ong, J. (1999). Global solvability and uniform decays of solutions to quasilinear equation with nonlinear boundary dissipation. Communications in Partial Differential Equations, 24 (11-12), 2069-2107. https://doi.org/10.1080/03605309908821495