Calculus of Variations and Geometric Measure Theory

J. F. Babadjian - V. Crismale

Dissipative boundary conditions and entropic solutions in dynamical perfect plasticity

created by crismale on 13 Dec 2019
modified on 19 Feb 2021


Published Paper

Inserted: 13 dec 2019
Last Updated: 19 feb 2021

Journal: J. Math. Pures Appl.
Year: 2021
Doi: 10.1016/j.matpur.2021.02.001

ArXiv: 1912.06106 PDF


We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic methods. The hyperbolic point of view enables one to derive a class of dissipative boundary conditions, somehow intermediate between homogeneous Dirichlet and Neumann ones. By using variational methods, we show the existence and uniqueness of solutions. Then we establish the equivalence between the original variational solutions and generalized entropic--dissipative ones, derived from a weak hyperbolic formulation for initial--boundary value Friedrichs' systems with convex constraints.