ON THE LONGTIME BEHAVIOR OF SOLUTIONS TO A MODEL FOR EPITAXIAL GROWTH

被引：0

作者：

Grasselli, Maurizio ^{[1
]}

Mola, Gianluca ^{[2
]}

Yagi, Atsushi ^{[3
]}

机构：

[1] Politecn Milan, Dipartimento Matemat F Brioschi, I-20133 Milan, Italy

[2] Univ Milan, Dipartimento Matemat F Enriques, I-20133 Milan, Italy

[3] Osaka Univ, Dept Appl Phys, Suita, Osaka 5650871, Japan

来源：

OSAKA JOURNAL OF MATHEMATICS | 2011年 / 48卷 / 04期

关键词：

THIN-FILM EPITAXY; SLOPE SELECTION; EQUATIONS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 delta Omega on a phase-space of L-2-type. This system possesses a global as well as an exponential attractor. In addition, if delta Omega is smooth enough, we show that every trajectory converges to a single equilibrium by means of a suitable Lojasiewicz-Simon inequality. An estimate of the convergence rate is also obtained.

引用

页码：987 / 1004

页数：18

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