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Unicité d’ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels. (Uniqueness of rarefaction waves for multidimensional quasilinear hyperbolic systems). (French) Zbl 0686.35072
Special solutions, rarefaction waves, for the quasilinear hyperbolic system: \[ v_ t+A_ 1(v)v_ x+A_ 2(v)v_ y=0;\quad x\in R,\quad y\in R^{n-2}, \] with \(C^{\infty}\) coefficients, and initial data discontinuous along a hypersurface are considered in this paper. A uniqueness result for sufficiently smooth solutions of this type is proved under suitable compatibility assumptions on the data. The required smoothness is connected to some index, which can be computed from the data. The special case of conservation laws is also considered.
Reviewer: D.Tataru

35L60 First-order nonlinear hyperbolic equations
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
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