Dissipative decomposition of partial differential equations

A general decomposition theorem that allows one to express an arbitrary differential polynomial as a sum of conservative, dissipative and higher order dissipative pieces is proved. The decomposition generalizes the dissipative decomposition of ordinary differential equations, but is no longer unique. The proof relies on the properties of certain generalizations of the standard symmetric polynomials known as multi-symmetric polynomials. The nonuniqueness of the decomposition is a consequence of the syzygies among the power sum multi-symmetric polynomials.