Deriving amplitude equations via evolutionary [Gamma]-convergence
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 1914 | |
dc.contributor.author | Mielke, Alexander | |
dc.date.accessioned | 2016-03-24T17:37:22Z | |
dc.date.available | 2019-06-28T08:16:26Z | |
dc.date.issued | 2014 | |
dc.description.abstract | We discuss the justification of the GinzburgLandau equation with real coefficients as an amplitude equation for the weakly unstable one-dimensional SwiftHohenberg equation. In contrast to classical justification approaches we employ the method of evolutionary [Gamma]-convergence by reformulating both equation as gradient systems. Using a suitable linear transformation we show [Gamma]-convergence of the associated energies in suitable function spaces. The limit passage of the time-dependent problem relies on the recent theory of evolutionary variational inequalities for families of uniformly convex functionals as developed by Daneri and Savare 2010. In the case of a cubic energy it suffices that the initial conditions converge strongly in L2, while for the case of a quadratic nonlinearity we need to impose weak convergence in H1. However, we do not need wellpreparedness of the initial conditions. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 0946-8633 | |
dc.identifier.uri | https://doi.org/10.34657/2210 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/3074 | |
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 | Ginzburg-Landau equation | eng |
dc.subject.other | Swift-Hohenberg equation | eng |
dc.subject.other | gradient systems | eng |
dc.subject.other | Gamma convergence | eng |
dc.subject.other | evolutionary variational inequality | eng |
dc.title | Deriving amplitude equations via evolutionary [Gamma]-convergence | 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 |
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