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Main Title: Global attractors of sixth order PDEs describing the faceting of growing surfaces
Author(s): Korzec, Maciek
Nayar, Piotr
Rybka, Piotr
Type: Research Paper
Abstract: A 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.
Subject(s): global attractor
long-time dynamics
Cahn-Hilliard type equation
high order PDE
Issue Date: 11-Mar-2013
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 35G25 Initial value problems for nonlinear higher-order PDE, nonlinear evolution equations
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2013, 05
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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