Symmetrization of systems of conservation equations and the converse to the condition of friedrichs and lax

摘要

The result of friedrichs and lax [Proc. Nat. Acad. Sci. U.S.A., 68,8,1686-1688, 1971] concluding that if the system of conservation equations implies the additional conservation equation (balance of entropy) then it can be symmetrized by prmulti- plication by the Hessian matrix of the entropy, is well known. Basic ingredients of the proof of the converse to this result can be found in the paper by Boilat [C.R.Acad. Sci. Paris, 278 A, 909-914 1974], however this converse has not been explicitly for- Mulated there and, as a consequence, it seems to be overlooked.