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Ondes soniques. (Sonic waves). (French) Zbl 0728.35068
The author considers hyperbolic systems of conservation laws in space dimension \(n\geq 1\). The aim of this paper is to investigate sonic waves, i.e. solutions with discontinuous first order derivatives; that can be regarded as natural extension of the investigation of Majda on shock fronts, i.e. discontinuous solutions. Basic examples are the sonic waves for the Euler systems of gas dynamics.
The obtained results are very general, including a detailed statement for the Cauchy problem; tools of the proofs are classical a priori estimates and a suitable variant of the paradifferential calculus of Bony.
Reviewer: L.Rodino (Torino)

35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
35S05 Pseudodifferential operators as generalizations of partial differential operators
76N15 Gas dynamics (general theory)