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This article considers the linear theory of thermoelastic materials with inner structure whose particles, in addition to the classical displacement and temperature fields, possess microtemperatures. We discuss some non-standard problems within the context of the dynamic boundary value problems. In fact, we use the Lagrange-Brun type identities combined with some differential inequalities in order to show that the final boundary value problem associated with the linear thermoelasticity withdoi:10.1080/01495739.2013.784117 fatcat:byskzegbnvfcnfdswtyq4nxvou