Dissipation rates and partition of energy in thermoelasticity

DOI10.1007/BF00251002zbMath0563.73007OpenAlexW2084132426MaRDI QIDQ1057679

George Dassios, Manoussos G. Grillakis

Publication date: 1984

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00251002

zbMATH Keywords

strain energylinear isotropic elasticityinitial velocityasymptotically equal to a convex combination of the kinetic and thermal energyequipartition energyhyperbolic equations of motioninitial displacementsinitial temperature distributionlowest nonvanishing momentsparabolic equation of energy conservationPartition of energyrate of decay of energysymmetry of the initial data

Mathematics Subject Classification ID

Thermodynamics in solid mechanics (74A15) Thermal effects in solid mechanics (74F05) Wave equation (35L05) Initial value problems for linear higher-order PDEs (35G10) Elastic materials (74B99) Higher-order parabolic equations (35K25)

Related Items (12)

Asymptotic equipartition rate for wave motion in an even number of space dimensions ⋮ Asymptotic behaviour in \(n\)-dimensional thermoelasticity ⋮ Existence and decay of weak solutions for systems arising in thermodynamics ⋮ Pullback dynamics for a class of non-autonomous Lamé thermoelastic system ⋮ On the wave propagation in the thermoelasticity theory with two temperatures ⋮ On the decay of a porous thermoelasticity type III with constant delay ⋮ Asymptotic behavior of solutions for the magneto-thermo-elastic system in \(\mathbb{R}^3\) ⋮ About analyticity for the coupled system of linear thermoviscoelastic equations ⋮ On the fundamental solution of the operator of dynamic linear thermoelasticity ⋮ The contact problem in thermoviscoelastic materials ⋮ Unnamed Item ⋮ Existence and exponential decay for contact problems in thermoelasiticity

Cites Work

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• Equipartition of energy in elastic wave propagation
• Eventual partition of conserved quantities in wave motion
• Partial differential equations. 3rd ed
• Equipartition of energy for anisotropic elastic waves
• Decay along non-bicharacteristic rays of solutions of first order hyperbolic systems
• On partition of energy for uniformly propagative systems
• An equipartition of energy theorem for weak solutions of evolutionary equations in Hilbert space: The Lagrange identity method
• Energy decay and partition for dissipative wave equations
• Abstract equipartition of energy theorems
• Eventual partition of conserved quantities for Maxwell's equations
• On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity
• An asymptotic property of solutions of wave equations. II
• Equipartition of energy in wave motion
• Equipartition of Energy in Scattering Theory
• Equipartition of energy for Maxwell’s equations
• Asymptotic equipartition of kinetic and strain energy for elastic waves in anisotropic media
• Equipartition of energy for higher-order hyperbolic equations
• Energy splitting
• Asymptotic Equipartition of Energy for Differential Equations in Hilbert Space
• Energy theorems for magnetoelastic waves in a perfectly conducting medium
• An Asymptotic Property of Solutions of Wave Equations

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