Spectral operators generated by damped hyperbolic equations
type: Item
instance of: scholarly article
title: Spectral operators generated by damped hyperbolic equations
zbMATH Open document ID: 0912.47016
DOI: 10.1007/BF01294159
author: Marianna A. Shubov
published in: Integral Equations and Operator Theory
publication date: 1999-05-03T00:00:00Z
review text: The author presents results on the spectral analysis of two nonselfadjoint operators which are the dynamics generators for systems governed by hyperbolic equations containing dissipative terms, namely, the nonhomogeneous damped string and the 3-dimensional damped wave equation with spacially nonhomogeneous spherically symmetric coefficients. Nonselfadjoint boundary conditions are imposed at the ends of a finite interval or on a sphere centered at the origin, respectively. It is shown that these operators are spectral in the sense of N. Dunford using the fact that the systems of root vectors form a Riesz basis in the corresponding energy spaces. Asymptotics of the spectra are obtained and results are stated on the property of the Riesz bases for the nonselfadjoint operator pencils associated with these operators.
Mathematics Subject Classification ID: 47B40
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 35L10
zbMATH DE Number: 1113570
zbMATH Keywords: spectral operators
zbMATH Keywords: damped hyperbolic equations
zbMATH Keywords: asymptotics of spectra
zbMATH Keywords: operator pencils
zbMATH Keywords: spectral analysis
zbMATH Keywords: nonselfadjoint operators
zbMATH Keywords: specially nonhomogeneous spherically symmetric coefficients
zbMATH Keywords: nonselfadjoint boundary conditions
zbMATH Keywords: Riesz bases
zbMATH Keywords: energy spaces
reviewed by: Rémi Vaillancourt
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01294159
OpenAlex ID: W1990654755
description: scientific article; zbMATH DE number 1113570