arXiv:1405.2223 Abstract | arXiv Analytics

arXiv:1405.2223 [math.AP]Abstract References Reviews Resources

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

Published 2014-05-09Version 1

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.

DOI: 10.1016/j.jde.2015.01.047

Categories: math.AP

Subjects: 35L65, 35Q74, 82B26, 74N20

Keywords: multi-phase models, 1d elastodynamics, non-local regularization, convergence, relative entropy stability theory

Related articles: Most relevant | Search more

arXiv:1205.5563 [math.AP] (Published 2012-05-24, updated 2013-04-30)

On the convergence of statistical solutions of the 3D Navier-Stokes-$α$ model as $α$ vanishes

Anne C. Bronzi, Ricardo M. S. Rosa

arXiv:0903.0984 [math.AP] (Published 2009-03-05)

$Γ$-convergence of some super quadratic functionals with singular weights

Giampiero Palatucci, Yannick Sire

arXiv:math/0509274 [math.AP] (Published 2005-09-13, updated 2006-06-12)