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December 2011 On the longtime behavior of solutions to a model for epitaxial growth
Maurizio Grasselli, Gianluca Mola, Atsushi Yagi
Osaka J. Math. 48(4): 987-1004 (December 2011).


We consider a fourth-order nonlinear parabolic type equation on a two-dimensional bounded domain $\Omega$. This equation governs the evolution of the height profile of a thin film in an epitaxial growth process. We show that such equation endowed with no-flux boundary conditions generates a dissipative dynamical system under very general assumptions on $\partial\Omega$ on a phase-space of $L^{2}$-type. This system possesses a global as well as an exponential attractor. In addition, if $\partial\Omega$ is smooth enough, we show that every trajectory converges to a single equilibrium by means of a suitable Łojasiewicz--Simon inequality. An estimate of the convergence rate is also obtained.


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Maurizio Grasselli. Gianluca Mola. Atsushi Yagi. "On the longtime behavior of solutions to a model for epitaxial growth." Osaka J. Math. 48 (4) 987 - 1004, December 2011.


Published: December 2011
First available in Project Euclid: 11 January 2012

zbMATH: 1233.35036
MathSciNet: MR2871290

Primary: 35B40 , 35B41 , 35K55

Rights: Copyright © 2011 Osaka University and Osaka City University, Departments of Mathematics


Vol.48 • No. 4 • December 2011
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