Abstract
We look at the structure of shocks for states near a locus where equations change type. Two basic models are considered: steady transonic flow, and models for unsteady change of type. Our result is that these two problems may be distinguished by the nature of the timelike directions and the forward light cone. This leads in a natural way to different candidates for admissible shocks in the two cases.
This work was performed during an extended visit to the IMA for the Nonlinear Waves program, and many of the ideas in this paper emerged from discussions with other participants. I’d like to thank them, as well as the IMA for hosting us.
Research supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 86–0088. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.
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Keyfitz, B.L. (1990). Shocks Near the Sonic Line: A Comparison between Steady and Unsteady Models for Change of 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_8
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DOI: https://doi.org/10.1007/978-1-4613-9049-7_8
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