Exponential decay of the energy of a nonlinear system of Klein–Gordon equations with localized dampings in bounded and unbounded domains

Ferreira, José da Silva

doi:10.3233/asy-1994-8105

Asymptotic Analysis

1994

DOI: 10.3233/asy-1994-8105

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Exponential decay of the energy of a nonlinear system of Klein–Gordon equations with localized dampings in bounded and unbounded domains

José da Silva Ferreira¹

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Cited by 8 publications

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Exponential stability of wave equations with potential and indefinite damping

Menz

2007

Journal of Differential Equations

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First, we consider the linear wave equation u ttThe damping function a is allowed to change its sign. If a := 1 L L 0 a(x) dx is positive and the spectrum of the operator (∂ xx − b) is negative, exponential stability is proved for small a − a L 2 . Explicit estimates of the decay rate ω are given in terms of a and the largest eigenvalue of (∂ xx − b). Second, we show the existence of a global, small, smooth solution of the corresponding nonlinear wave equation u tt − σ (u x ) x + a(x)u t + b(x)u = 0, if, additionally, the negative part of a is small enough compared with ω.

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Exponential stability of wave equations with potential and indefinite damping

Menz

2007

Journal of Differential Equations

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Asymptotic stability for a strongly coupled Klein-Gordon system in an inhomogeneous medium with locally distributed damping

Cavalcanti

Mansouri

et al. 2020

Journal of Differential Equations

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Asymptotic stability for a generalized nonlinear Klein-Gordon system

Buriol

Delatorre

Martinez

et al. 2021

Journal of Differential Equations

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Exponential decay of the energy of a nonlinear system of Klein–Gordon equations with localized dampings in bounded and unbounded domains

Cited by 8 publications

References 0 publications

Exponential stability of wave equations with potential and indefinite damping

Exponential stability of wave equations with potential and indefinite damping

Asymptotic stability for a strongly coupled Klein-Gordon system in an inhomogeneous medium with locally distributed damping

Asymptotic stability for a generalized nonlinear Klein-Gordon system

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