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Decay of solutions of the wave equation with localized nonlinear damping and trapped rays

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  • We prove some decay estimates of the energy of the wave equation governed by localized nonlinear dissipations in a bounded domain in which trapped rays may occur. The approach is based on a comparison with the linear damped wave equation and an interpolation argument. Our result extends to the nonlinear damped wave equation the well-known optimal logarithmic decay rate for the linear damped wave equation with regular initial data.
    Mathematics Subject Classification: Primary: 35L05, 35L71; Secondary: 35B40, 35B35.

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