Calculus of Variations and Geometric Measure Theory

R. Rossi - G. Savaré

A characterization of Energetic and BV solutions to one-dimensional rate-independent systems

created by rossi on 31 Aug 2011


Submitted Paper

Inserted: 31 aug 2011

Year: 2011


The notion of BV solution to a rate-independent system was introduced in to describe the vanishing viscosity limit (in the dissipation term) of doubly nonlinear evolution equations. Like energetic solutions in the case of convex energies, BV solutions provide a careful description of rate-independent evolution driven by nonconvex energies, and in particular of the energetic behavior of the system at jumps.

In this paper we study both notions in the one-dimensional setting and we obtain a full characterization of BV and energetic solutions for a broad family of energy functionals. In the case of monotone loadings we provide a simple and explicit characterization of their solutions, which allows for a direct comparison of the two concepts.