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Hyperbolic structure for a simplified model of dynamical perfect plasticity

By Jean-François Babadjian and Clément Mifsud

Abstract

International audienceThis paper is devoted to confront two different approaches to the problem of dynam-ical perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs' system enables one to derive admissible hyperbolic boundary conditions. Using variational methods, we show the well-posedness of this problem in a suitable weak measure theoretic setting. Thanks to the property of finite speed propagation, we establish a new regularity result for the solution in short time. Finally, we prove that this variational solution is actually a solution of the hyperbolic formulation in a suitable dissipative/entropic sense, and that a partial converse statement holds under an additional time regularity assumption for the dissipative solutions

Topics: [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
Publisher: Springer Verlag
Year: 2017
DOI identifier: 10.1007/s00205-016-1045-4
OAI identifier: oai:HAL:hal-01256139v1
Provided by: Hal-Diderot

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