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Young measure solutions for nonconvex elastodynamics. (English) Zbl 1039.74005

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)].

MSC:

74B20 Nonlinear elasticity
74H20 Existence of solutions of dynamical problems in solid mechanics
49Q20 Variational problems in a geometric measure-theoretic setting
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