Young measure solutions for nonconvex elastodynamics

Marc Oliver Rieger

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Submission date: 14. Oct. 2000
Pages: 20
published in: SIAM journal on mathematical analysis, 34 (2003) 6, p. 1380-1398 (electronic) 
DOI number (of the published article): 10.1137/S0036141001392141
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Abstract:
In this paper we study the nonlinear equation of elastodynamics where the free energy functional is allowed to be nonconvex. We define the notion of Young measure solutions for this problem and prove an existence theorem in this class. This can be used as a model for the evolution of microstructures in crystals.
We furthermore introduce an optional coupling with a parabolic equation and prove existence of a Young measure solution for this system.