Hyperbolic structure for a simplified model of dynamical perfect plasticity

Jean-François Babadjian (1) , Clément Mifsud (1)

1 LJLL - Laboratoire Jacques-Louis Lions

This 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.

Domaines: Equations aux dérivées partielles [math.AP]

Jean-François Babadjian, Clément Mifsud. Hyperbolic structure for a simplified model of dynamical perfect plasticity. Archive for Rational Mechanics and Analysis, 2017, 223 (2), pp.761-815. ⟨10.1007/s00205-016-1045-4⟩. ⟨hal-01256139⟩