Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] Peter D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 11. MR 0350216 (50 #2709)
  • [2] R. Courant and K. O. Friedrichs, Supersonic flow and shock waves, Springer-Verlag, New York-Heidelberg, 1976. Reprinting of the 1948 original; Applied Mathematical Sciences, Vol. 21. MR 0421279 (54 #9284)
  • [3] L. Hörmander, Linear partial differential operators, Springer-Verlag, Berlin, 1963.
  • [4] Marvin Shinbrot and Robert R. Welland, The Cauchy-Kowalewskaya theorem, J. Math. Anal. Appl. 55 (1976), no. 3, 757–772. MR 0492756 (58 #11827)
  • [5] 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.
  • [6] Robert D. Richtmyer, Principles of advanced mathematical physics. Vol. I, Springer-Verlag, New York-Heidelberg, 1978. Texts and Monographs in Physics. MR 517399 (84h:00024a)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35L65, 76N15

Retrieve articles in all journals with MSC: 35L65, 76N15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0825712-4
PII: S 0002-9947(1986)0825712-4
Keywords: Conservation laws, hyperbolic, Euler equations, majorization
Article copyright: © Copyright 1986 American Mathematical Society