Abstract
For the equations of elastodynamics with polyconvex stored energy, and some related simpler systems, we define a notion of a dissipative measure-valued solution and show that such a solution agrees with a classical solution with the same initial data, when such a classical solution exists. As an application of the method we give a short proof of strong convergence in the continuum limit of a lattice approximation of one dimensional elastodynamics in the presence of a classical solution. Also, for a system of conservation laws endowed with a positive and convex entropy, we show that dissipative measure-valued solutions attain their initial data in a strong sense after time averaging.
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Demoulini, S., Stuart, D.M.A. & Tzavaras, A.E. Weak–Strong Uniqueness of Dissipative Measure-Valued Solutions for Polyconvex Elastodynamics. Arch Rational Mech Anal 205, 927–961 (2012). https://doi.org/10.1007/s00205-012-0523-6
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DOI: https://doi.org/10.1007/s00205-012-0523-6