Uniform energy decay for a wave equation with partially supported nonlinear boundary dissipation without growth restrictions
The article refers to a mixed problem for the wave equation, on a bounded domain in a \(d\)-dimensional space, with a nonlinear boundary damping. The goal of the paper is to derive energy decay rates for this nonlinear problem. One proves estimates for different types of damping: linearly bounded near infinity, superlinear near infinity, sublinear near infinity, superlinear at infinity with a stricter regularity assumption as well as some combinations of damping at the origin and infinity. The study is based on the following technique: associate the energy functional to the nonlinear problem, start with the linear PDE problem, prove observability inequality, built an appropriate nonlinear differential equation and estimate solutions for this one.
scientific article; zbMATH DE number 5552666