Reduction of balance laws to conservation laws by means of equivalence transformations

Abstract

A class of partial differential equations (a conservation law and two balance laws), with three independent variables and involving six arbitrary continuously differentiable functions, is considered in the framework of equivalence transformations. These are point transformations of differential equations involving arbitrary elements and live in an augmented space of independent, dependent, and additional variables representing values taken by the arbitrary elements. Projecting the admitted symmetries into the space of independent and dependent variables, we determine some finite transformations mapping the system of balance laws to an equivalent one with the same differential structure but involving different arbitrary elements; in particular, we are interested in finding an equivalent autonomous system of conservation laws. It is shown how the results apply to some physical problems.