TY - JOUR
T1 - Global Attractors of Sixth Order PDEs Describing the Faceting of Growing Surfaces
AU - Korzec, M. D.
AU - Nayar, P.
AU - Rybka, P.
N1 - Publisher Copyright:
© 2015, The Author(s).
PY - 2016/3/1
Y1 - 2016/3/1
N2 - 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, as well as its reduced one-dimensional version. These equations are expressed in terms of the slopes (Formula presented.) and (Formula presented.) to establish the existence of global, connected attractors for both equations. Since unique solutions are guaranteed for initial conditions in (Formula presented.), we consider the solution operator (Formula presented.), to gain our results. We prove the necessary continuity, dissipation and compactness properties.
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, as well as its reduced one-dimensional version. These equations are expressed in terms of the slopes (Formula presented.) and (Formula presented.) to establish the existence of global, connected attractors for both equations. Since unique solutions are guaranteed for initial conditions in (Formula presented.), we consider the solution operator (Formula presented.), to gain our results. We prove the necessary continuity, dissipation and compactness properties.
KW - Anisotropic surface energy
KW - Cahn-Hilliard type equation
KW - Global attractor
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U2 - 10.1007/s10884-015-9510-6
DO - 10.1007/s10884-015-9510-6
M3 - Article
AN - SCOPUS:84957840712
SN - 1040-7294
VL - 28
SP - 49
EP - 67
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
IS - 1
ER -