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

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.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1986-0825712-4

Keywords:
Conservation laws,
hyperbolic,
Euler equations,
majorization

Article copyright:
© Copyright 1986
American Mathematical Society