## 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
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### References:

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