Spectrum and analyticity of semigroups arising in elasticity theory and hydromechanics
type: Item
instance of: scholarly article
title: Spectrum and analyticity of semigroups arising in elasticity theory and hydromechanics
zbMATH Open document ID: 1175.47036
author: Birgit Jacob
author: Carsten Trunk
published in: Semigroup Forum
publication date: 2009-10-02T00:00:00Z
full work available at URL: dbt mods 00011137
review text: Cauchy problems for a second order linear differential operator equation \[ \ddot{z}(t)+A_{0}z(t)+D\dot{z}(t)=0 \] in a Hilbert space \(H\) are studied. Equations of this kind arise for example in elasticity and hydrodynamics. It is assumed that \(A _{0}\) is a uniformly positive operator and that \(A_0^{-1/2}DA_0^{-1/2}\) is a bounded accretive operator in \(H\). The location of the spectrum of the corresponding semigroup generator is described and sufficient conditions for analyticity are given.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47N50
zbMATH DE Number: 5610563
zbMATH Keywords: block operator matrices
zbMATH Keywords: analytic semigroups
zbMATH Keywords: spectrum
zbMATH Keywords: second order equations
zbMATH Keywords: accretive operators
MaRDI profile type: Publication
OpenAlex ID: W2086579271
cites work: Well posedness for damped second order systems with unbounded input operators
cites work: Q3365603
cites work: A mathematical model for linear elastic systems with structural damping
cites work: Proof of extensions of two conjectures on structural damping for elastic systems
cites work: Characterization of domains of fractional powers of certain operators arising in elastic systems, and applications
cites work: The Influence of Timing on RadiationDamage to Cell Populations
cites work: One-Parameter Semigroups for Linear Evolution Equations
cites work: The functional calculus for sectorial operators
cites work: Exponential stability of semigroups associated with some operator models in mechanics.
cites work: Exponential decay of solution energy for equations associated with some operator models of mechanics
cites work: On the Mathematical Model for Linear Elastic Systems with Analytic Damping
cites work: Q5753617
cites work: Location of the spectrum of operator matrices which are associated to second order equations
cites work: Minimum-Phase Infinite-Dimensional Second-Order Systems
cites work: Analyticity and Riesz basis property of semigroups associated to damped vibrations
cites work: Q4110164
cites work: Operator approach to linear problems of hydrodynamics. Vol. 1: Self-adjoint problems for an ideal fluid
cites work: Q4297796
cites work: Q4718340
cites work: How to Get a Conservative Well-Posed Linear System Out of Thin Air. Part II. Controllability and Stability
cites work: Energy decay of damped systems
cites work: How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance
DOI: 10.1007/S00233-009-9148-Y
description: scientific article; zbMATH DE number 5610563