WIAS Preprint No. 1347, (2008)

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



Authors

  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Rossi, Riccarda
  • Savaré, Giuseppe

2010 Mathematics Subject Classification

  • 35K55 49Q20 58E99

Keywords

  • Metric flow, rate-independent systems, quasistatic evolution, vanishing-viscosity limit, parametrized metric solution, approximable solutions

Abstract

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.

Appeared in

  • Discrete Contin. Dyn. Syst., 25 (2009) pp. 585--615.

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