Balanced-Viscosity solutions for multi-rate systems
dc.bibliographicCitation.volume | 2001 | |
dc.contributor.author | Mielke, Alexander | |
dc.contributor.author | Rossi, Riccarda | |
dc.contributor.author | Savaré, Giuseppe | |
dc.date.accessioned | 2016-03-24T17:37:02Z | |
dc.date.available | 2019-06-28T08:12:41Z | |
dc.date.issued | 2014 | |
dc.description.abstract | Several mechanical systems are modeled by the static momentum balance for the displacement u coupled with a rate-independent flow rule for some internal variable z. We consider a class of abstract systems of ODEs which have the same structure, albeit in a finite-dimensional setting, and regularize both the static equation and the rate-independent flow rule by adding viscous dissipation terms with coefficients α and , where 0<<1 and α>0 is a fixed parameter. Therefore for α different from 1 the variables u and z have different relaxation rates. We address the vanishing-viscosity analysis as tends to 0 in the viscous system. We prove that, up to a subsequence, (reparameterized) viscous solutions converge to a parameterized curve yielding a Balanced Viscosity solution to the original rate-independent system and providing an accurate description of the system behavior at jumps. We also give a reformulation of the notion of Balanced Viscosity solution in terms of a system of subdifferential inclusions, showing that the viscosity in u and the one in z are involved in the jump dynamics in different ways, according to whether α >1, α=1, or 0<α<1. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2039 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2884 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.ispartofseries | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2001, ISSN 2198-5855 | eng |
dc.rights.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. | eng |
dc.rights.license | 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. | ger |
dc.subject | Generalized gradient systems | eng |
dc.subject | vanishing-viscosity approach | eng |
dc.subject | energy-dissipation principle | eng |
dc.subject | jump curves | eng |
dc.subject.ddc | 510 | eng |
dc.title | Balanced-Viscosity solutions for multi-rate systems | eng |
dc.type | report | eng |
dc.type | Text | eng |
dcterms.bibliographicCitation.journalTitle | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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