Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics
Analysis of PDEs
2012-06-12 v1
Abstract
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.
Cite
@article{arxiv.1109.6686,
title = {Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics},
author = {Sophia Demoulini and David Stuart and Athanasios Tzavaras},
journal= {arXiv preprint arXiv:1109.6686},
year = {2012}
}