Conservation laws and potential symmetries of systems of diffusion equations

We classify local first-order conservation laws for a class of systems of nonlinear diffusion equations. The derived conservation laws are used to construct the set of inequivalent potential systems for the class under consideration. Four potential systems are investigated from the Lie point of view and new potential symmetries are obtained. An example of the reduction of a system of diffusion equations with respect to a potential symmetry generator is given. A nonlinear system that has applications in plasma physics is linearized using infinite-dimensional potential symmetries.