Global existence and decay to the initial-boundary value problem for the Kirchhoff type quasilinear wave equation with a nonlinear localized dissipation

摘要

We prove the existence of global small amplitude decaying solutions to the initial-boundary value problem for the Kirchhoff type quasilinear wave equations with a localized nonlinear dissipation and a source term. Since our dissipation is effective possibly only on a neighbourhood of a certain part of the boundary and also time dependent the decay rate is very delicate.