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arXiv · 1405.2223

Relative entropy in multi-phase models of 1d elastodynamics: Convergence of a non-local to a local model

Jan Giesselmann
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Abstract

In this paper we study a local and a non-local regularization of the system of nonlinear elastodynamics with a non-convex energy. We show that solutions of the non-local model converge to those of the local model in a certain regime. The arguments are based on the relative entropy framework and provide an example how local and non-local regularizations may compensate for non-convexity of the energy and enable the use of the relative entropy stability theory -- even if the energy is not quasi- or poly-convex.

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Jan Giesselmann. 2014-05-09. Relative entropy in multi-phase models of 1d elastodynamics: Convergence of a non-local to a local model. https://arxiv.org/abs/1405.2223

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