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

Shubov, Marianna A.

Asymptotic Anal. 16, No. 3-4, 245-272 (1998).

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.

Reviewer: Anton Deitmar (Heidelberg)

MSC:

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

Keywords:

spatially non-homogeneous spherical symmetric coefficients; non-conservative boundary conditions; asymptotic formulas; non-selfadjoint quadratic operator pencils