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Formation of singularities in solutions to nonlinear hyperbolic equations. (English) Zbl 0564.35070
In this paper the author considers mainly a system of conservation laws as follows: I) In one space dimension, it is strictly hyperbolic, or II) in several space dimensions, it can be reduced to a symmetric system. Assuming some structural assumptions, the author gives the existing results on formation of singularities for the above systems. The interesting point is to introduce certain averaged quantities and to avoid the reliance upon characteristics.
Reviewer: M.Tsuji

MSC:
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
35L70 Second-order nonlinear hyperbolic equations
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