Conservation laws of evolution systems

For evolution systems of differential equations, conserved currents, in particular trivial ones, are described in terms of their densities. A formula that can be regarded as an analog of Noether's theorem for non-Lagrangian systems is derived. An isomorphism is constructed between the space of conservation laws, i.e., the equivalence classes of the conserved currents with respect to the trivial currents, and the solution space of a certain strongly overdetermined system of linear differential equations.