On an application of Tikhonovs fixed point theorem to a nonlocal Cahn-Hilliard type system modeling phase separation
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2181 | |
dc.contributor.author | Colli, Pierluigi | |
dc.contributor.author | Gilardi, Gianni | |
dc.contributor.author | Sprekels, Jürgen | |
dc.date.accessioned | 2016-12-13T10:46:53Z | |
dc.date.available | 2019-06-28T08:26:41Z | |
dc.date.issued | 2015 | |
dc.description.abstract | This paper investigates a nonlocal version of a model for phase separation on an atomic lattice that was introduced by P. Podio-Guidugli in Ric. Mat. 55 (2006) 105-118. The model consists of an initial-boundary value problem for a nonlinearly coupled system of two partial differential equations governing the evolution of an order parameter p and the chemical potential my. Singular contributions to the local free energy in the form of logarithmic or ouble-obstacle potentials are admitted. In contrast to the local model, which was studied by P. Podio-Guidugli and the present authors in a series of recent publications, in the nonlocal case the equation governing the evolution of the order parameter contains in place of the Laplacian a nonlocal expression that originates from nonlocal contributions to the free energy and accounts for possible long-range interactions between the atoms. It is shown that just as in the local case the model equations are well posed, where the technique of proving existence is entirely different: it is based on an application of Tikhonovs fixed point theorem in a rather unusual separable and reflexive Banach space. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2815 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/3494 | |
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 | Cahn–Hilliard system | eng |
dc.subject.other | nonlocal energy | eng |
dc.subject.other | phase separation | eng |
dc.subject.other | singular potentials | eng |
dc.subject.other | initialboundary value problem | eng |
dc.subject.other | Tikhonov’s fixed point theorem | eng |
dc.title | On an application of Tikhonovs fixed point theorem to a nonlocal Cahn-Hilliard type system modeling phase separation | 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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