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Quasiconvex Elastodynamics: Weak‐Strong Uniqueness for Measure‐Valued Solutions
Author(s) -
Koumatos Konstantinos,
Spirito Stefano
Publication year - 2019
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21801
Subject(s) - quasiconvex function , uniqueness , mathematics , convexity , novelty , function (biology) , measure (data warehouse) , mathematical analysis , entropy (arrow of time) , pure mathematics , regular polygon , subderivative , convex optimization , computer science , geometry , philosophy , physics , theology , quantum mechanics , database , evolutionary biology , financial economics , economics , biology
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.