Spectral Analysis for a System of Wave Equations and Applications

ABSTRACT The energy of solution of the wave equation unidimensional with a punctual interior damping at is decreasing to zero if and only if . We study in this paper the case of , we calculate the limit of the energy, and we identify the best rate of decay with the spectral abscissa of the underlying semigroup generator. We identify the spectral abscissa as in terms of the largest modulus of the roots of a polynomial.