Thermoelasticity with second sound—exponential stability in linear and non‐linear 1‐d

Abstract

Abstract We consider linear and non‐linear thermoelastic systems in one space dimension where thermal disturbances are modelled propagating as wave‐like pulses travelling 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 with 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 non‐linear system. Copyright © 2002 John Wiley & Sons, Ltd.