Asymptotic stability in thermoelectromagnetism with memory

A model describing a linear homogeneous dielectric with memory which obeys the Cattaneo-Maxwell law for the heat conduction is presented. The restrict ions on the constitutive functionals are found as a direct consequence of t he Second Law of Thermodynamics and some free energy potentials exhibited. Such potentials allow to determine a domain of dependence theorem for the f irst-order integro-differential system of equations governing the evolution of the thermoelectromagnetic radiation. The dissipativity due to the memor y and to the heat conduction allows to establish some estimates on the asym ptotic behaviour and prove the exponential decay of the solution of the sys tem in absence of external sources. Copyright (C) 1999 John Wiley & Sons, L td.