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Corpus ID: 202719582

Exponential decay for the semilinear wave equation with localized Kelvin-Voight damping

@article{Rojas2019ExponentialDF,
title={Exponential decay for the semilinear wave equation with localized Kelvin-Voight damping},
author={M. R. A. Rojas and M. M. Cavalcanti and Wellington J. Corr{\^e}a and V. Cavalcanti and V. G. Martinez and A. Vicente},
journal={arXiv: Analysis of PDEs},
year={2019}
}

In the present paper, we are concerned with the semilinear viscoelastic wave equation subject to a locally distributed dissipative effect of Kelvin-Voigt type, posed on a bounded domain with smooth boundary. We begin with an auxiliary problem and we show that its solution decays exponentially in the weak phase space. The method of proof combines an observability inequality and unique continuation properties. Then, passing to the limit, we recover the original model and prove its global… CONTINUE READING