Wave propagation and breaking in multidimensional magnetogasdynamic flows

Lustman, Levi; Geffen, Nima

doi:10.1007/bf01590841

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Introduction2

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1980

2023

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Cited by 4 publications

(2 citation statements)

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“…They have found that there is always one wave-the "slow" wave-which does not develop into a shock. This is remarkable, since the nonbreaking waves are the exception rather than the rule [3,4,12]. We shall show that their result follows, in fact, from the one dimensionality assumption.…”

Section: Introductionmentioning

confidence: 73%

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A Note on Nonbreaking Waves in Hyperelastic Materials

Lustman

1980

Stud Appl Math

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This note treats the evolution of waves on hyperelastic materials, due to initial jump discontinuities in the gradient of strain. In general, these discontinuities become unbounded in finite time, leading to discontinuous strain. There are, however, certain cases in which the gradient jump remains finite for all times. We show here that the class of materials admitting such exceptional waves is fairly large, including Hadamard materials and generalized Hooke materials. An earlier example of Jeffrey and Teymur [6] is also discussed and reset in a more general framework.

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Section: Introductionmentioning

confidence: 73%

“…When this happens, lower order derivatives become discontinuous-for first order systems, this corresponds to shock formation. The critical surfaces-times and places-of wave breaking may be computed explicitly, by analytical or numerical means [3][4][5][6]11,12,15].…”

Section: Introductionmentioning

confidence: 99%