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**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

### MSC:

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 |

### Keywords:

invariant submanifolds; quasilinear first order partial differential system; conservation laws; geometry of a wave curve; shock wave curve; rarefaction wave curve
Full Text:
DOI

### References:

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