Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term (Q1878501)

For the wave equation with a source term \[ u_{tt}- \Delta u = | u| ^{p}u \quad \text{in } \Omega \times (0,\infty) \] it is proved the existence and uniform decay rates of the energy by assuming a nonlinear feedback \(\beta(u_{t})\) acting on the boundary provided that \(\beta\) has necessarily not a polynomial growth near the origin.