Quasiconvex Elastodynamics: Weak‐Strong Uniqueness for Measure‐Valued Solutions
Konstantinos Koumatos, Stefano Spirito · Communications on Pure and Applied Mathematics · 2018
Abstract A weak‐strong uniqueness result is proved for measure‐valued solutions to the system of conservation laws arising in elastodynamics. The main novelty brought forward by the present work is that the underlying stored‐energy function of the material is assumed to be strongly quasiconvex. The proof employs tools from the calculus of variations to establish general convexity‐type bounds on quasiconvex functions and recasts them in order to adapt the relative entropy method to quasiconvex elastodynamics. © 2018 Wiley Periodicals, Inc.