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A class of partial differential equations (a conservation law and fourbalance laws), with four independent variables and involving sixteen arbitrarycontinuously differentiable functions, is considered in the framework ofequivalence transformations. These are point transformations of differentialequations involving arbitrary elements and live in an augmented space ofindependent, dependent and additional variables representing values taken bythe arbitrary elements. Projecting the admitted symmetries into the space ofindependent and dependent variables, we determine some finite transformationsmapping the system of balance laws to an equivalent one with the samedifferential structure but involving different arbitrary elements; inparticular, the target system we want to recover is an autonomous system ofconservation laws. An application to a physical problem is considered.

Reduction of balance laws in (3+1)--dimensions to autonomous conservation laws by means of equivalence transformations