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Title: Modeling solutions with jumps for rate-independent systems on metric spaces
Authors: Mielke, AlexanderRossi, RiccardaSavaré, Giuseppe
Issue Date: 2008
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1347, 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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.
Keywords: Metric flow; rate-independent systems; quasistatic evolution; vanishing-viscosity limit; parametrized metric solution; approximable solutions
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik



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