Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Admissibility criteria for shock wave solutions of a system of conservation laws of mixed type

Michael Shearera1

a1 Department of Mathematics, Duke University, Durham, North Carolina 27706, U.S.A.

Synopsis

The following system of conservation laws is considered:

S0308210500015948_eqnU1

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)