a1 Department of Mathematics, Duke University, Durham, North Carolina 27706, U.S.A.
The following system of conservation laws is considered:
where σ: ℝ→ℝ is a smooth function monotonically increasing except in an interval. Two criteria for the admissibility of shocks are shown to be independent in the sense that there are shocks satisfying each and violating the other. This contrasts with the corresponding situation for strictly hyperbolic systems (σ'(u)>0 for all u), for which the two criteria are equivalent.
(Received January 28 1982)