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|Title:||On an application of Tikhonovs fixed point theorem to a nonlocal Cahn-Hilliard type system modeling phase separation|
|Authors:||Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen|
|Published in:||Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2181, ISSN 2198-5855|
|Publisher:||Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik|
|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.|
|Keywords:||Cahn–Hilliard system; nonlocal energy; phase separation; singular potentials; initialboundary value problem; Tikhonov’s fixed point theorem|
|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.|
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.
|Appears in Collections:||Mathematik|
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