publication . Article . Other literature type . 2000

Young measure solutions for nonconvex elastodynamics

Marc Oliver Rieger;
Open Access
  • Published: 01 Jan 2000 Journal: SIAM Journal on Mathematical Analysis, volume 34, pages 1,380-1,398 (issn: 0036-1410, eissn: 1095-7154, Copyright policy)
  • Publisher: Society for Industrial & Applied Mathematics (SIAM)
Abstract
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 the existence of a Young measure solution for this system.
Subjects
free text keywords: Mathematical Physics and Mathematics, Hyperbolic partial differential equation, Mathematical analysis, Existence theorem, Probability measure, Young measure, Nonlinear system, Parabola, Weak convergence, Energy functional, Mathematics
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