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@techreport { 11303_15791,
author = {Korzec, Maciek AND Nayar, Piotr AND Rybka, Piotr},
title = {Global attractors of sixth order PDEs describing the faceting of growing surfaces},
institution = {Technische UniversitÃ¤t Berlin},
year = {2013},
doi = {10.14279/depositonce-14564},
url = {http://dx.doi.org/10.14279/depositonce-14564},
keywords = {global attractor, long-time dynamics, Cahn-Hilliard type equation, high order PDE, faceting},
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.}
}