Asymptotics of spectrum and eigenfunctions for nonselfadjoint operators generated by radial nonhomogeneous damped wave equations.(English)Zbl 0938.35113

From the abstract: We consider an infinite sequence of radial wave equations obtained by the separation of variables in the spherical coordinates from the 3-dimensional damped wave equation with spatially non-homogeneous spherical symmetric coefficients. The non-conservative boundary conditions are given on the sphere $$|x|=a$$. Our main objects of interest are the non-selfadjoint operators in the energy space of 2-component initial data, which are the dynamics generators for the systems governed by the aforementioned equations and boundary conditions. Our main results are precise asymptotic formulas for the complex eigenvalues and eigenfunctions of these operators and the corresponding non-selfadjoint quadratic operator pencils.

MSC:

 35P20 Asymptotic distributions of eigenvalues in context of PDEs 35L05 Wave equation 47F05 General theory of partial differential operators