Systems of conservation laws with invariant submanifolds. (English) Zbl 0559.35046

The author considers a quasilinear first order partial differential system of conservation laws in one space dimension: \(\partial_ tU+\partial_ xF(U)=0\) where U and F are \(R^ N\) vectors; \(U\equiv U(x,t)\). The aim of the paper is to characterize necessary and sufficient conditions on the geometry of a wave curve in order that a shock wave curve coincides with its associate rarefaction wave curve. Particular emphasis is devoted to the case when \(U\in R^ 2\).
Reviewer: T.Ruggeri


35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
76S05 Flows in porous media; filtration; seepage
76T99 Multiphase and multicomponent flows
35L80 Degenerate hyperbolic equations
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