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

  • Michael Shearer (a1)

Synopsis

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.

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3Korteweg, D. J.Sur la forme que prennent les equations du mouvement des fluides si Ton tient compte des forces capillaires par des variations de densite considerables mais continues et sur la theorie de la capillarite dans l'hypothese d'une variation continue de la densite. Arch. Neerl. Sci. 6 (1901), 124.
4Mock, M. S.. Systems of conservation laws of mixed type. J. Differential Equations 37 (1980), 7088.
5Shearer, M.. The Riemann problem for a class of conservation laws of mixed type. Differential Equations, to appear.
6Slemrod, M.. Admissibility criteria for propagating phase boundaries in a van der Waalsfluid. Arch. Rational Mech. Anal., to appear.

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

  • Michael Shearer (a1)

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