Exponential decay for the semilinear wave equation with localized Kelvin-Voight damping
Analysis of PDEs
2019-09-24 v1
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.
Keywords
Cite
@article{arxiv.1909.10044,
title = {Exponential decay for the semilinear wave equation with localized Kelvin-Voight damping},
author = {Maria Rosario Astudillo Rojas and Marcelo M. Cavalcanti and Wellington J. Correa and Valeria N. Domingos Cavalcanti and Victor H. Gonzalez Martinez and Andre Vicente},
journal= {arXiv preprint arXiv:1909.10044},
year = {2019}
}
Comments
27 pages, 5 figures