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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.

MSC:
35A25Other special methods (PDE)
80A20Heat and mass transfer, heat flow
35C05Solutions of PDE in closed form
58J70Invariance and symmetry properties
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