Decay rate of solutions to Timoshenko system with past history in unbounded domains

DOI10.1007/S00245-016-9336-6zbMath1378.35297OpenAlexW2264915618MaRDI QIDQ2013929

Belkacem Said-Houari, Maisa Khader

Publication date: 10 August 2017

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00245-016-9336-6

zbMATH Keywords

energy methodLyapunov functionaldecay rateFourier spaceintegral estimatesTimoshenko systemregularity lossGurtin-Pipkin heat conduction

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Asymptotic behavior of solutions to PDEs (35B40) Integro-partial differential equations (45K05) Thermal effects in solid mechanics (74F05) Groups and semigroups of linear operators (47D03) Linear constitutive equations for materials with memory (74D05) PDEs in connection with mechanics of deformable solids (35Q74) Integro-partial differential equations (35R09)

Related Items (13)

General decay of the Moore-Gibson-Thompson equation with viscoelastic memory of type II ⋮ Optimal decay rate of solutions to Timoshenko system with past history in unbounded domains ⋮ Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with microtemperature effect ⋮ Decay rate of the solutions to the Cauchy problem of the Bresse system in thermoelasticity of type III with distributed delay ⋮ Decay rates of strongly damped Infinite laminated beams ⋮ New decay rates for a Cauchy thermoelastic laminated Timoshenko problem with interfacial slip under Fourier or Cattaneo laws ⋮ Some \(L^2(\mathbb{R})\)-norm and \(L^1(\mathbb{R})\)-norm decay estimates for Cauchy Timoshenko type systems with a frictional damping or an infinite memory ⋮ On the decay rates for two Cauchy thermoelastic laminated Timoshenko problems of type III with interfacial slip ⋮ On the stability of a laminated Timoshenko problem with interfacial slip in the whole space under frictional dampings or infinite memories ⋮ Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay ⋮ Stability and instability results for Cauchy laminated Timoshenko-type systems with interfacial slip and a heat conduction of Gurtin-Pipkin's law ⋮ Optimal decay rate for the Cauchy problem of the standard linear solid model with Gurtin-Pipkin thermal law ⋮ Well-posedness and decay property of regularity-loss type for the Cauchy problem of the standard linear solid model with Gurtin–Pipkin thermal law

Cites Work

• The effect of the wave speeds and the frictional damping terms on the decay rate of the Bresse system
• The stability number of the Timoshenko system with second sound
• Damping by heat conduction in the Timoshenko system: Fourier and Cattaneo are the same
• On the stability of Timoshenko systems with Gurtin-Pipkin thermal law
• A general theory of heat conduction with finite wave speeds
• Asymptotic stability in viscoelasticity
• Decay property of Timoshenko system in thermoelasticity
• DECAY PROPERTY OF REGULARITY-LOSS TYPE FOR DISSIPATIVE TIMOSHENKO SYSTEM
• DECAY PROPERTY OF REGULARITY-LOSS TYPE AND NONLINEAR EFFECTS FOR DISSIPATIVE TIMOSHENKO SYSTEM
• Decay rates and global existence for semilinear dissipative Timoshenko systems
• Heat waves

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