On the existence of intermediate magnetohydrodynamic shock waves |
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Authors: | Konstantin Mischaikow Harumi Hattori |
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Affiliation: | (1) Department of Mathematics, Michigan State University, 48823 East Lansing, Michigan;(2) School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia, 30332;(3) Present address: Department of Mathematics, West Virginia University, 26506 Morgantown, West Virginia |
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Abstract: | We consider the questions related to the structure of shock waves for a system of magnetohydrodynamic equations. Using Conley's connection matrix, we recover and extend earlier results due to C. Conley and J. Smoller. In particular, we give a simpler proof of the existence of fast and slow shocks with structure. We also demonstrate that for some viscosity parameters intermediate shocks occur. Furthermore, under an assumption of transversality, we show that there exist multi-parameter families of these intermediate shocks.This research was done while both authors were visiting the Lefschetz Center for Dynamical Systems at Brown University.Supported in part by the NSF under Grant DMS-8507056.Supported in part by AFOSR 87-0347. |
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Keywords: | Conley Index connection matrix heteroclinic orbits magnetohydrodynamics shock waves traveling waves |
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