Equivalence transformations and symmetries for a heat conduction model

Abstract

In the framework of Extended Thermodynamics, we consider the unidimensional case of a non-linear system of partial differential equations describing the heat conduction in a rigid body and removing the well known paradox of thermal pulses propagating with infinite speed. Because of the strong non-linearity of the model we look for an invariant classification via equivalence transformations. Some general results concerned with the equivalence transformations for 2 × 2 quasilinear systems of partial differential equations are shown. Special classes of exact solutions for the system considered are obtained and discussed.