Cavalcanti, Marcelo M.; Domingos Cavalcanti, Valéria N.; Fukuoka, Ryuichi; Pampu, Ademir B.; Astudillo, María Uniform decay rate estimates for the semilinear wave equation in inhomogeneous medium with locally distributed nonlinear damping. (English) Zbl 1397.35025 Nonlinearity 31, No. 9, 4031-4064 (2018). Summary: We consider the semilinear wave equation posed in an inhomogeneous medium \(\Omega\) with smooth boundary \(\partial\Omega\) subject to a nonlinear damping distributed around a neighborhood \(\omega\) of the boundary according to the geometric control condition. We show that the energy of the wave equation goes uniformly to zero for all initial data of finite energy phase-space. Cited in 17 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 74J30 Nonlinear waves in solid mechanics 93D15 Stabilization of systems by feedback 35R01 PDEs on manifolds 35L71 Second-order semilinear hyperbolic equations Keywords:geometric control condition PDFBibTeX XMLCite \textit{M. M. 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