Calculus of Variations and Geometric Measure Theory

A. Mielke - R. Rossi - G. Savaré

Modeling solutions with jumps for rate-independent systems on metric spaces

created by rossi on 30 Jun 2008
modified by savare on 25 Feb 2009


Accepted Paper

Inserted: 30 jun 2008
Last Updated: 25 feb 2009

Journal: Discrete Contin. Dyn. Syst.
Year: 2008


Rate-independent systems allow for solutions with jumps that need additional modeling. Here we suggest a formulation that arises as limit of viscous regularization of the solutions in the extended state space. Hence, our parametrized metric solutions of a rate-independent system are absolutely continuous mappings from a parameter interval into the extended state space. Jumps appear as generalized gradient flows during which the time is constant. The closely related notion of BV solutions is developed afterwards. Our approach is based on the abstract theory of generalized gradient flows in metric spaces, and comparison with other notions of solutions is given.

Keywords: Gradient flows, Rate independent evolutions, Viscosity approximation, Parametrized solutions