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The author derives the heat propagation equation for forced convection replacing Fourier's law by a constitutive equation generalising Cattaneo's one. Then, for the above mentioned equation, she establishes a uniqueness theorem for finite domains.
We establish a uniqueness theorem for the heat propagation by natural convection governed by the Boussinesq equations, when we replace Fourier's law by Cattaneo-Fox' constitutive equation in bounded domains.
Employing the weight function method, we establish a uniqueness theorem for the heat propagation by natural convection governed by the Boussinesq equations when we replace Fourier’s constitutive equation by Cattaneo-Fox’ one, on an exterior domain. We prove the theorem without boundedness assumptions on the velocity gradient and on the temperature.
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