Spectral analysis and stabilization of one dimensional wave equation with singular potential

Abstract

In this paper, we are interested in a boundary damped wave problem with a singular potential. Using a careful spectral analysis, asymptotic expressions of the eigenvalues and eigenvectors of the system operator are derived in terms of the dissipative coefficient and the potential. The Riesz basis property of eigenfunctions and generalized eigenfunctions is also studied. As a consequence, we obtained the exponential stability.