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

Maria Rosario Astudillo Rojas; Marcelo M. Cavalcanti; Wellington J. Correa; Valeria N. Domingos Cavalcanti; Victor H. Gonzalez Martinez; Andre Vicente

arXiv · 1909.10044

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

Maria Rosario Astudillo Rojas·Marcelo M. Cavalcanti·Wellington J. Correa·Valeria N. Domingos Cavalcanti·Victor H. Gonzalez Martinez·Andre Vicente

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Abstract

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 existence as well as the exponential stability.

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BibTeX RIS

Maria Rosario Astudillo Rojas, Marcelo M. Cavalcanti, Wellington J. Correa, Valeria N. Domingos Cavalcanti, Victor H. Gonzalez Martinez, Andre Vicente. 2019-09-22. Exponential decay for the semilinear wave equation with localized Kelvin-Voight damping. https://arxiv.org/abs/1909.10044

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