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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
References
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 291 (1985), 451-485
  • MSC: Primary 35L60; Secondary 35A20, 58G17
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0800248-4
  • MathSciNet review: 800248