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Admissible wave fans in nonlinear hyperbolic systems. (English) Zbl 0707.35091

The quasi-linear hyperbolic system

t U(x,t)+ x F(U(x,t))=0

is investigated. The author describes several well known conditions for admissible shock waves and wave fans (i.e. solutions U(x,t) of the form U(x,t)=V(x/t))·

The main object of the paper is the discussion of the entropy rate admissibility criterion for wave fans, which was introduced by the author [J. Differ. Equations 14, 202-212 (1973; Zbl 0262.35038)]. In particular, it is shown that the entropy condition implies the admissibility criterion of Liu for wave fans of moderate strength.

Reviewer: L.Brüll

35L67Shocks and singularities
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