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Study of non-uniqueness and instability for convex materials.

机译:研究凸材料的非唯一性和不稳定性。

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There are stability analyses of two-dimensional plane shock waves which show the existence of unstable shock fronts for some equations of state. We present numerical evidence that these unstable two-dimensional shocks are also unstable in one dimension, at least in the sense that the Lax-Friedrichs difference scheme does not have a steady asymptotic traveling wave connecting the shocked and unshocked states. When there is instability there are also multiple solutions of the Riemann problem. In the typical case of two stable solutions and one unstable one, which of the stable ones is selected seems to depend on mesh size or the initial profile. If there is a physical selection principle, Lax-Friedrichs does not obey it. 11 refs., 13 figs. (ERA citation 15:036295)

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