Thermoelasticity with second sound : exponential stability in linear and nonlinear 1-d

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2001
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We consider linear and nonlinear thermoelastic systems in one space dimension where thermal disturbances are modeled propagating as wave-like pulses traveling at finite speed. This removal of the physical paradox of infinite propagation speed in the classical theory of thermoelasticity within Fourier's law is achieved using Cattaneo's law for heat conduction. For different boundary conditions, in particular for those arising in pulsed laser heating of solids, the exponential stability of the now purely, but slightly damped, hyperbolic linear system is proved. A comparison to classical hyperbolic-parabolic thermoelasticity is given. For Dirichlet type boundary conditions - rigidly clamped, constant temperature - the global existence of small, smooth solutions and the exponential stability are proved for a nonlinear system.

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ISO 690RACKE, Reinhard, 2001. Thermoelasticity with second sound : exponential stability in linear and nonlinear 1-d
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@unpublished{Racke2001Therm-680,
  year={2001},
  title={Thermoelasticity with second sound : exponential stability in linear and nonlinear 1-d},
  author={Racke, Reinhard}
}
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    <dcterms:abstract xml:lang="eng">We consider linear and nonlinear thermoelastic systems in one space dimension where thermal disturbances are modeled propagating as wave-like pulses traveling at finite speed. This removal of the physical paradox of infinite propagation speed in the classical theory of thermoelasticity within Fourier's law is achieved using Cattaneo's law for heat conduction. For different boundary conditions, in particular for those arising in pulsed laser heating of solids, the exponential stability of the now purely, but slightly damped, hyperbolic linear system is proved. A comparison to classical hyperbolic-parabolic thermoelasticity is given. For Dirichlet type boundary conditions - rigidly clamped, constant temperature - the global existence of small, smooth solutions and the exponential stability are proved for a nonlinear system.</dcterms:abstract>
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