Repository: DepositOnce â€“ institutional repository for research data and publications of TU Berlin https://depositonce.tu-berlin.de
TY - RPRT
AU - Korzec, Maciek
AU - Nayar, Piotr
AU - Rybka, Piotr
PY - 2013
TI - Global attractors of sixth order PDEs describing the faceting of growing surfaces
DO - 10.14279/depositonce-14564
UR - http://dx.doi.org/10.14279/depositonce-14564
PB - Technische UniversitÃ¤t Berlin
LA - en
AB - 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.
KW - global attractor
KW - long-time dynamics
KW - Cahn-Hilliard type equation
KW - high order PDE
KW - faceting
ER -