Propagation of singularities for nonstrictly hyperbolic semilinear systems in one space dimension

Micheli, Lucio

doi:10.1090/S0002-9947-1985-0800248-4

Propagation of singularities for nonstrictly hyperbolic semilinear systems in one space dimension
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by Lucio Micheli PDF

Trans. Amer. Math. Soc. 291 (1985), 451-485 Request permission

Abstract:

We consider the creation and propagation of singularities in the solutions of semilinear nonstrictly hyperbolic systems in one space dimension when the initial data has jump discontinuities. We show that singularities travelling along characteristics can branch at points of degeneracy of the vector fields on all other forward characteristics. We prove a lower bound for the strength of these new singularities, and we give an example showing that our result cannot be improved in general.

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