A fourth-order parabolic equation modeling epitaxial thin film growth |
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Authors: | Belinda B King Oliver Stein Michael Winkler |
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Institution: | a Interdisciplinary Center for Applied Mathematics, Virginia Tech, Blacksburg, VA 24061, USA b Department of Mathematics C, Aachen University, Aachen, Germany c Department of Mathematics I, Aachen University, Aachen, Germany |
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Abstract: | We study the continuum model for epitaxial thin film growth from Phys. D 132 (1999) 520-542, which is known to simulate experimentally observed dynamics very well. We show existence, uniqueness and regularity of solutions in an appropriate function space, and we characterize the existence of nontrivial equilibria in terms of the size of the underlying domain. In an investigation of asymptotical behavior, we give a weak assumption under which the ω-limit set of the dynamical system consists only of steady states. In the one-dimensional setting we can characterize the set of steady states and determine its unique asymptotically stable element. The article closes with some illustrative numerical examples. |
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Keywords: | Thin film growth Fourth-order diffusion Large time behavior Steady states |
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