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

Kim Dang Phung | Zendy

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

Author(s) -

Kim Dang Phung

Publication year - 2011

Publication title -

mathematical control and related fields

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.658

H-Index - 21

eISSN - 2156-8472

pISSN - 2156-8499

DOI - 10.3934/mcrf.2011.1.251

Subject(s) - wave equation , bounded function , logarithm , nonlinear system , physics , domain (mathematical analysis) , damped wave , mathematical analysis , energy (signal processing) , interpolation (computer graphics) , radiation damping , mathematics , classical mechanics , quantum mechanics , motion (physics)

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.

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