Polynomial stability of one‐dimensional wave equation with local degenerate Kelvin–Voigt damping and discontinuous coefficients

Abstract

AbstractIn this paper, we study the stability of one‐dimensional wave equation with local degenerate Kelvin–Voigt damping and discontinuous coefficients. The domain of the wave equation is a bounded interval. The support of the damping coefficient function is a subinterval of the bounded interval, which does not include the endpoints of the bounded interval. The damping coefficient function behaves like power functions near the endpoints of the subinterval. When the coefficients of the wave equation satisfy suitable regularity assumption, by the frequency domain method, we show that the energy of the wave equation decays polynomially and the decay rate depends on the exponents of power functions.