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Browsing by Author "Slemrod, M."

Now showing 1 - 3 of 3
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    Lax-Friedrichs and the Viscosity-Capillarity Criterion
    (1983) Slemrod, M.
    It has been shown by Lax some time ago that for hyperbolic conversation laws solutions obtained as limits of the Lax-Friedrichs finite difference scheme will actually satisfy an "entropy" admissibility criterion. The goal of this paper is to attempt to extend Lax's idea to a form which is amenable to mixed problems as well, e.g. the dynamics of a van der Waals fluid. Specifically, we compare shocks obtained by the Lax-Friedrichs scheme with those permitted by the viscosity-capillarity criterion of [2, 3]. We show that for isothermal motion it is expected that shocks produced by Lax-Friedrichs will satisfy the viscosity-capillarity criterion.
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    Spatial Chaos in a Van der Waals Fluid Due to Periodic Thermal Fluctuations
    (1983) Slemrod, M.; Marsden, J.E.
    This paper applies the Mel'nikov technique to prove the existence of deterministic chaos in two problems for a Van der Waals fluid. The first problem shows that temporal chaos results as a result of small time periodic fluctuations about a subcritical temperature when the fluid is initially quenched in the unstable spinoidal region. The second problem shows that spatial chaos arises from small spatially periodic flunctions in an infinite tube of fluid if the ambient pressure is appropriately chosen.