Authors: | Andreia, Merlin Meyer, Christian |
Title: | On a lack of stability of parametrized BV solutions to rate-independent systems with non-convex energies and discontinuous loads |
Language (ISO): | en |
Abstract: | We consider a rate-independent system with nonconvex energy under discontinuous external loading. The underlying space is finite dimensional and the loads are functions in BV([0, T]; ℝ^d). We investigate the stability of various solution concepts w.r.t. a sequence of loads converging weakly∗ in BV([0, T]; ℝ^d) with a particular emphasis on the so-called normalized, pparametrized balanced viscosity solutions. By means of two counterexamples, it is shown that common solution concepts are not stable w.r.t. weak∗ convergence of loads in the sense that a limit of a sequence of solutions associated with these loads need not be a solution corresponding to the load in the limit. We moreover introduce a new solution concept, which is stable in this sense, but our examples show that this concept necessarily allows “solutions” that are physically meaningless. |
Subject Headings: | rate-independent systems local solutions paramterized BV solutions stability of solutions discontinuous loads |
URI: | http://hdl.handle.net/2003/42125 http://dx.doi.org/10.17877/DE290R-23958 |
Issue Date: | 2023-08 |
Appears in Collections: | Ergebnisberichte des Instituts für Angewandte Mathematik |
Files in This Item:
File | Description | Size | Format | |
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Ergebnisbericht Nr. 667.pdf | DNB | 503.93 kB | Adobe PDF | View/Open |
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