Weak-Strong Uniqueness of Dissipative Measure-Valued Solutions for Polyconvex Elastodynamics

Sophia Demoulini*, David M.A. Stuart, Athanasios Tzavaras

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

42 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)927-961
Number of pages35
JournalArchive for Rational Mechanics and Analysis
Volume205
Issue number3
DOIs
StatePublished - Aug 1 2012

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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