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Admissibility of Solutions to the Riemann Problem for Systems of Mixed Type

-transonic small disturbance theory-

  • Conference paper
Nonlinear Evolution Equations That Change Type

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 27))

Abstract

The transonic small disturbance equation is put into the context of first order systems of conservation laws. The admissibility of shock solutions is studied via Lax inequalities, entropy inequalities, the viscosity method, Oleǐnik’s E-condition, Liu’s extended entropy condition and a class of generalized entropy inequalities. This includes the case of mixed-type shocks (elliptic-hyperbolic). The admissibility condition of transonic small disturbance theory is shown to arise from an additional conservation law different from the one used in the case of the classical p-system in isentropic gas dynamics.

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This research was supported by a grant of the Stiftung Volkswagenwerk, Germany

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Author information

Authors and Affiliations

  1. Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, 7000, Stuttgart 80, Germany

    Gerald Warnecke

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  1. Gerald Warnecke
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Editors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, Texas, 77204, USA

    Barbara Lee Keyfitz

  2. Department of Mathematics, North Carolina State University, Raleigh, North Carolina, 27695, USA

    Michael Shearer

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Warnecke, G. (1990). Admissibility of Solutions to the Riemann Problem for Systems of Mixed Type. In: Keyfitz, B.L., Shearer, M. (eds) Nonlinear Evolution Equations That Change Type. The IMA Volumes in Mathematics and Its Applications, vol 27. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9049-7_19

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  • DOI: https://doi.org/10.1007/978-1-4613-9049-7_19

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9051-0

  • Online ISBN: 978-1-4613-9049-7

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