Rieger, Marc Oliver Young measure solutions for nonconvex elastodynamics. (English) Zbl 1039.74005 SIAM J. Math. Anal. 34, No. 6, 1380-1398 (2003). This paper is concerned with the study of nonlinear equations of elastodynamics where the free energy functional is allowed to be nonconvex. The authors prove the existence of Young measure solutions for nonconvex elasticity equations in arbitrary space dimensions under some growth conditions on the free energy, and study a model problem where the nonconvex elasticity is coupled with a parabolic equation. The authors extend the concept of Young measure solutions to this hyperbolic-parabolic system, and prove the existence of Young measure solutions. Related results can be found in S. Demoulini [SIAM J. Math. Anal. 27, No. 2, 376–403 (1996; Zbl 0851.35066)] and in D. Kinderlehrer and P. Pedregal [SIAM J. Math. Anal. 23, No. 1, 1–19 (1992 Zbl 0757.49014)]. Reviewer: Nicolae Pop (Baia Mare) Cited in 12 Documents MSC: 74B20 Nonlinear elasticity 74H20 Existence of solutions of dynamical problems in solid mechanics 49Q20 Variational problems in a geometric measure-theoretic setting Keywords:nonlinear elasticity; nonconvex variational problems; free energy functional; existence; parabolic equation; hyperbolic-parabolic system Citations:Zbl 0851.35066; Zbl 0757.49014 PDFBibTeX XMLCite \textit{M. O. Rieger}, SIAM J. Math. Anal. 34, No. 6, 1380--1398 (2003; Zbl 1039.74005) Full Text: DOI