Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics

Details Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics

2011-09-29

arxiv.org/abs/1109.6686v1

Mathematics

Analysis of PDEs

Scientific paper

For the equations of elastodynamics with polyconvex stored energy, and some related simpler systems, we define a notion of 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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