Energy decay for a nonlinear generalized Klein-Gordon equation in exterior domains with a nonlinear localized dissipative term (Q455008)

The author derives an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation in exterior domains with a nonlinear localized dissipation. His equation includes an absorbing term like \(|u|^{\alpha }u, \alpha \geq 0\), and can be regarded as a generalized Klein-Gordon equation at least if \(\alpha \) is close to 0. He proves that this observation plays an essential role in the author's argument.