In this paper we consider the Green and Lindsay nonclassical model for inhomogeneous anisotropic thermoelastic bodies with two relaxation times, which depend on space variables. We obtain a variational formulation for the initial-boundary value problem corresponding to the Green–Lindsay model. On the basis of the variational formulation we define the spaces of vector-valued distributions corresponding to the initial-boundary value problem and by applying suitable a priori estimates we prove the existence and uniqueness of the solution, an energy equality, and the continuous dependence of the solution on given data.
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