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Transactions of the American Mathematical Society

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A convergent series expansion for hyperbolic systems of conservation laws


Author: Eduard Harabetian
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
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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 [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1986-0825712-4
Keywords: Conservation laws, hyperbolic, Euler equations, majorization
Article copyright: © Copyright 1986 American Mathematical Society

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