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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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A convergent series expansion for hyperbolic systems of conservation laws
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by Eduard Harabetian PDF
Trans. Amer. Math. Soc. 294 (1986), 383-424 Request permission

Abstract:

We consider the discontinuous piecewise analytic initial value problem for a wide class of conservation laws that includes the full three-dimensional Euler equations. The initial interaction at an arbitrary curved surface is resolved in time by a convergent series. Among other features the solution exhibits shock, contact, and expansion waves as well as sound waves propagating on characteristic surfaces. The expansion waves correspond to the one-dimensional rarefactions but have a more complicated structure. The sound waves are generated in place of zero strength shocks, and they are caused by mismatches in derivatives.
References
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    • A. Majda, The stability of multi-dimensional shock fronts and The existence of multi-dimensional shock fronts, Mem. Amer. Math. Soc. Nos. 275 and 281, 1983.
  • Robert D. Richtmyer, Principles of advanced mathematical physics. Vol. I, Texts and Monographs in Physics, Springer-Verlag, New York-Heidelberg, 1978. MR 517399
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 294 (1986), 383-424
  • MSC: Primary 35L65; Secondary 76N15
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0825712-4
  • MathSciNet review: 825712