  A class of partial differential equations (a conservation law and four
balance laws), with four independent variables and involving sixteen 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, the target system we want to recover is an autonomous system of
conservation laws. An application to a physical problem is considered.
