Non-homogeneous thermoelastic Timoshenko systems
type: Item
instance of: scholarly article
title: Non-homogeneous thermoelastic Timoshenko systems
zbMATH Open document ID: 1391.35045
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2017-12-08T00:00:00Z
full work available at URL: http://www.locus.ufv.br/handle/123456789/22045
review text: The authors consider the problem \[ \begin{cases} \rho_1\varphi _{tt}-\left( k(\varphi _{x}+\psi )\right) _x+\left(m\theta \right) _{x}=0,\;\text{ in }(0,l)\times \mathbb{R}^{+}, \\ \rho _{2}\psi _{tt}-\left( b\psi _{x}\right) _{x}+k(\varphi _{x}+\psi )-m\theta =0,\;\text{ in }(0,l)\times \mathbb{R}^{+}, \\ \rho _{3}\theta _{t}-\left( c\theta _{x}\right) _{x}+m(\varphi _{xt}+\psi_{t})=0,\;\text{ in }(0,l)\times \mathbb{R}^{+},\end{cases} \] with non-homogeneous coefficients and with initial conditions and Dirichlet boundary conditions. They proved that under the condition \[ \frac{k(x)}{\rho_1(x)}=\frac{b(x)}{\rho _2(x)} \] for \(x\) in some open subinterval of \((0,l),\) the system is exponentially stable. In case this condition is violated, then the stability is of polynomial type. To this end, they use the resolvent characterization of polynomial and exponential stability of linear semigroups methods. These results improve and extend considerably several existing results in the literature.
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 74D05
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 35G46
zbMATH DE Number: 6816650
zbMATH Keywords: non-homogeneous coefficients
zbMATH Keywords: exponential stability
zbMATH Keywords: polynomial stability
zbMATH Keywords: Dirichlet boundary conditions
author: Margareth Alves
author: M. A. Jorge Silva
author: To Fu Ma
author: Jaime E. Muñoz Rivera
reviewed by: N.-E. Tatar
MaRDI profile type: Publication
OpenAlex ID: W2586972273
cites work: Stability to weakly dissipative Timoshenko systems
cites work: Stability to 1-D thermoelastic Timoshenko beam acting on shear force
cites work: Energy decay for Timoshenko systems of memory type.
cites work: Stabilization of the nonuniform Timoshenko beam
cites work: Optimal polynomial decay of functions and operator semigroups
cites work: Uniform decay rates for the energy of Timoshenko system with the arbitrary speeds of propagation and localized nonlinear damping
cites work: On the stability of Timoshenko systems with Gurtin-Pipkin thermal law
cites work: Energy decay to Timoshenko's system with thermoelasticity of type III
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: Boundary Control of the Timoshenko Beam
cites work: Modeling, analysis and control of dynamic elastic multi-link structures
cites work: Q4239302
cites work: Global existence and optimal decay rates for the Timoshenko system: the case of equal wave speeds
cites work: Rates of decay to non homogeneous Timoshenko model with tip body
cites work: Mildly dissipative nonlinear Timoshenko systems -- global existence and exponential stability.
cites work: Wave splitting of the Timoshenko beam equation in the time domain
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: On the Spectrum of C 0 -Semigroups
cites work: Exponential stability for the Timoshenko system with two weak dampings
cites work: Damping by heat conduction in the Timoshenko system: Fourier and Cattaneo are the same
cites work: The stability number of the Timoshenko system with second sound
cites work: Stabilisation de la poutre de Timoshenko
cites work: Exponential stability of the linearized nonuniform Timoshenko beam
DOI: 10.1007/S00574-017-0030-3
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description: scientific article; zbMATH DE number 6816650