Effects of history and heat models on the stability of thermoelastic Timoshenko systems
type: Item
instance of: scholarly article
title: Effects of history and heat models on the stability of thermoelastic Timoshenko systems
zbMATH Open document ID: 1467.35052
published in: Journal of Differential Equations
publication date: 2021-01-08T00:00:00Z
full work available at URL: urn:nbn:de:bsz:352-2-1tfhswxpw76d78
review text: The Timoshenko system is a linear PDE system of two perturbed wave equations in dimension one. The two unknowns represent the vertical displacement and the rotation angle of a beam. In this paper the authors study a Timoshenko system with two damping mechanisms. A first damping term is a (nonlinear) history term given by an integral over time with an exponentially decaying kernel. A second damping mechanism is related to thermal effects: the system is complemented by a heat-like equation where the heat conduction is governed by a so-called Cattaneo law. The authors prove that the system is exponentially stable if the history term is present, while there is no exponential stability without history term.
reviewed by: Giuliano Lazzaroni
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35Q79
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 74H40
Mathematics Subject Classification ID: 35R09
Mathematics Subject Classification ID: 35G46
zbMATH DE Number: 7291335
zbMATH Keywords: exponential stability
zbMATH Keywords: Cattaneo law
zbMATH Keywords: parabolic-hyperbolic system
zbMATH Keywords: two damping mechanisms
author: M. A. Jorge Silva
author: Reinhard Racke
MaRDI profile type: Publication
OpenAlex ID: W3035896039
cites work: Stability to 1-D thermoelastic Timoshenko beam acting on shear force
cites work: On a Timoshenko system with thermal coupling on both the bending moment and the shear force
cites work: On Modeling and Uniform Stability of a Partially Dissipative Viscoelastic Timoshenko System
cites work: Invariance of decay rate with respect to boundary conditions in thermoelastic Timoshenko systems
cites work: Non-homogeneous thermoelastic Timoshenko systems
cites work: Energy decay for Timoshenko systems of memory type.
cites work: General stability of memory-type thermoelastic Timoshenko beam acting on shear force
cites work: Tauberian Theorems for the Laplace-Stieltjes Transform
cites work: Asymptotic stability of Schrödinger semigroups: Path integral methods
cites work: Who developed the so-called Timoshenko beam theory?
cites work: The Timoshenko system with history and Cattaneo law
cites work: Uniform decay of energy for a porous thermoelasticity system with past history
cites work: Optimal rates of decay in 2-d thermoelasticity with second sound
cites work: On the stability of damped Timoshenko systems: Cattaneo versus Fourier law
cites work: Spectral Theory for Contraction Semigroups on Hilbert Space
cites work: Q4407520
cites work: Q3722900
cites work: Q4239302
cites work: General decay for a porous thermoelastic system with memory: the case of equal speeds
cites work: General decay for a porous-thermoelastic system with memory: the case of nonequal speeds
cites work: Stability of Timoshenko systems with past history
cites work: Mildly dissipative nonlinear Timoshenko systems -- global existence and exponential stability.
cites work: Addendum to: ``Qualitative aspects of solutions in resonators''
cites work: The stability number of the Timoshenko system with second sound
cites work: On the Spectrum of C 0 -Semigroups
cites work: Stabilisation de la poutre de Timoshenko
cites work: Energy decay for Porous-thermo-elasticity systems of memory type
DOI: 10.1016/J.JDE.2020.11.041
description: scientific article; zbMATH DE number 7291335