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dc.contributor.authorKorzec, Maciek
dc.contributor.authorNayar, Piotr
dc.contributor.authorRybka, Piotr
dc.date.accessioned2021-12-17T10:11:42Z-
dc.date.available2021-12-17T10:11:42Z-
dc.date.issued2013-03-11
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15791-
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14564-
dc.description.abstractA spatially two-dimensional sixth order PDE describing the evolution of a growing crystalline surface h(x,y,t) that undergoes faceting is considered with periodic boundary conditions, such as its reduced one-dimensional version. These equation are expressed in terms of the slopes $u_1=h_{x}$ and $u_2=h_y$ to establish the existence of global, connected attractors for both of the equations. Since unique solutions are guaranteed for initial conditions in $\dot H^2_{per}$, we consider the solution operator $S(t): \dot H^2_{per} \rightarrow \dot H^2_{per}$, to gain the results. We prove the necessary continuity, dissipation and compactness properties.en
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherglobal attractoren
dc.subject.otherlong-time dynamicsen
dc.subject.otherCahn-Hilliard type equationen
dc.subject.otherhigh order PDEen
dc.subject.otherfacetingen
dc.titleGlobal attractors of sixth order PDEs describing the faceting of growing surfacesen
dc.typeResearch Paperen
tub.accessrights.dnbfreeen
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2013, 05en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
dc.type.versionsubmittedVersionen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften » Inst. Mathematikde
tub.subject.msc200035G25 Initial value problems for nonlinear higher-order PDE, nonlinear evolution equationsen
Appears in Collections:Technische Universität Berlin » Publications

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