In this paper we study the behaviour of a three-dimensional linear thermoelectromagnetic material, which has constitutive equations with memory effects for both the heat flux and the electric current density. We develop a linearized theory of thermodynamics, in which context we are able to introduce a maximal free energy defined in the frequency domain. Using this free energy a domain of dependence is obtained. Moreover, we prove a theorem of uniqueness, existence and asymptotic stability.
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