On evolutionary [Gamma]-convergence for gradient systems : in memory of Eduard, Waldemar, and Elli Mielke
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 1915 | |
dc.contributor.author | Mielke, Alexander | |
dc.date.accessioned | 2016-03-24T17:37:22Z | |
dc.date.available | 2019-06-28T08:16:25Z | |
dc.date.issued | 2014 | |
dc.description.abstract | In these notes we discuss general approaches for rigorously deriving limits of generalized gradient flows. Our point of view is that a generalized gradient system is defined in terms of two functionals, namely the energy functional E and the dissipation potential R or the associated dissipation distance. We assume that the functionals depend on a small parameter and that the associated gradient systems have solutions u. We investigate the question under which conditions the limits u of (subsequences of) the solutions u are solutions of the gradient system generated by the [Gamma]-limits E0 and R0. Here the choice of the right topology will be crucial awell as additional structural conditions. We cover classical gradient systems, where R is quadratic, and rate-independent systems as well as the passage from classical gradient to rate-independent systems. Various examples, such as periodic homogenization, are used to illustrate the abstract concepts and results. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2799 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/3073 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | 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.ddc | 510 | eng |
dc.subject.other | Variational evolution | eng |
dc.subject.other | energy functional | eng |
dc.subject.other | dissipation potential | eng |
dc.subject.other | dissipation distance | eng |
dc.subject.other | gradient flows | eng |
dc.subject.other | Gamma convergence | eng |
dc.subject.other | well-prepared initial conditions | eng |
dc.subject.other | rate-independent systems | eng |
dc.subject.other | abstract chain-rule | eng |
dc.subject.other | enerty-dissipation balance integrated evolutionary variational estimate | eng |
dc.subject.other | energetic solutions | eng |
dc.title | On evolutionary [Gamma]-convergence for gradient systems : in memory of Eduard, Waldemar, and Elli Mielke | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- 787868965.pdf
- Size:
- 890.76 KB
- Format:
- Adobe Portable Document Format
- Description: