Equivalence transformations and symmetries for a heat conduction model. (English) Zbl 0911.35005

The authors consider one dimensional heat flow in a rigid body in the framework of Extended Thermodynamics, which means, roughly, the Fourier law of heat conduction is replaced by Cattaneo’s extension thereof. They obtain a highly nonlinear model of partial differential equations, which under certain conditions is hyperbolic. An invariant classification via equivalence transformations is sought. Special classes of exact solutions are obtained and discussed. Fourier’s theory is shown to be the limiting case of the theory under consideration when a certain parameter is allowed to tend to zero. Both the model and the analysis are complicated.


35A25 Other special methods applied to PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
35C05 Solutions to PDEs in closed form
58J70 Invariance and symmetry properties for PDEs on manifolds
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