High Frequency Vibrations in a Stiff Problem
Miguel Lobo, Eugenia Pérez · Mathematical Models and Methods in Applied Sciences · 1997
The stiff problem here considered models the vibrations of a body consisting of two materials, one of them very stiff with respect to the other. We study the asymptotic behavior of the eigenvalues and eigenfunctions of the corresponding spectral problem, when the stiffness constant of only one of the materials tends to 0. We show that the associated operator has a discrete spectrum "converging", in a certain sense, towards a continuous spectrum in [0,∞) corresponding to an operator. We also provide information on the structure of the eigenfunctions associated with the high frequencies.