Abstract
This paper is concerned with the study of the uniform decay rates of the energy associated with the wave equation subject to a locally distributed viscoelastic dissipation and a nonlinear frictional damping
where \({\Omega\subset\mathbb{R}^n, n\geq 2}\) is an unbounded open set with finite measure and unbounded smooth boundary \({\partial\Omega = \Gamma}\). Supposing that the localization functions satisfy the “competitive” assumption \({a(x)+b(x)\geq\delta>0}\) for all \({x\in \Omega}\) and the relaxation function g satisfies certain nonlinear differential inequalities introduced by Lasiecka et al. (J Math Phys 54(3):031504, 2013), we extend to our considered domain the prior results of Cavalcanti and Oquendo (SIAM J Control Optim 42(4):1310–1324, 2003). In addition, while in Cavalcanti and Oquendo (2003) the authors just consider exponential and polynomial decay rate estimates, in the present article general decay rate estimates are obtained.
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PhD students at UEM, partially supported by CAPES and a grant of CNPq, Brazil.
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Dias Silva, F.R., Nascimento, F.A.F. & Rodrigues, J.H. General decay rates for the wave equation with mixed-type damping mechanisms on unbounded domain with finite measure. Z. Angew. Math. Phys. 66, 3123–3145 (2015). https://doi.org/10.1007/s00033-015-0547-5
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DOI: https://doi.org/10.1007/s00033-015-0547-5