On a lack of stability of parametrized BV solutions to rate-independent systems with non-convex energies and discontinuous loads

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dc.contributor.authorAndreia, Merlin
dc.contributor.authorMeyer, Christian
dc.date.accessioned2023-10-09T12:57:28Z
dc.date.available2023-10-09T12:57:28Z
dc.date.issued2023-08
dc.description.abstractWe 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.en
dc.identifier.issn2190-1767
dc.identifier.urihttp://hdl.handle.net/2003/42125
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-23958
dc.language.isoen
dc.relation.ispartofseriesErgebnisberichte des Instituts für Angewandte Mathematik;667
dc.subjectrate-independent systemsen
dc.subjectlocal solutionsen
dc.subjectparamterized BV solutionsen
dc.subjectstability of solutionsen
dc.subjectdiscontinuous loadsen
dc.subject.ddc610
dc.titleOn a lack of stability of parametrized BV solutions to rate-independent systems with non-convex energies and discontinuous loadsen
dc.typeText
dc.type.publicationtypePreprint
dcterms.accessRightsopen access
eldorado.secondarypublicationfalse

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