Sharp stability of a string with local degenerate Kelvin–Voigt damping

This paper is on the asymptotic behavior of the elastic string equation with localized degenerate Kelvin–Voigt damping where on , and on for . It is known that the optimal decay rate of solution is in the limit case and exponential for . When , the damping coefficient is continuous, but its derivative has a singularity at the interface . In this case, the best known decay rate is , which fails to match the optimal one at . In this paper, we...