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
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
收藏
页码:987 / 1004
页数:18
相关论文
共 16 条
[1]  
[Anonymous], NONLINEAR FUNCTIONAL
[2]  
Cazenave T., 1998, OXFORD LECT SERIES M, V13
[3]  
CHILL R., 2006, P 5 EUROPEAN MAGHREB, P25
[4]   Exponential attractors for a nonlinear reaction-diffusion system in R3 [J].
Efendiev, M ;
Miranville, A ;
Zelik, S .
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 330 (08) :713-718
[5]  
Feireisl E., 2000, J DYN DIFFER EQU, V12, P647, DOI DOI 10.1023/A:1026467729263
[6]  
Fujimura H., 2008, MAT MEKH INFORM, V10, P75
[7]  
Fujimura H., 2008, INT MATH FORUM, V3, P1803
[8]  
Fujimura H., 2009, SCI MATH JPN, V69, P295
[9]   A simple unified approach to some convergence theorems of L. Simon [J].
Jendoubi, MA .
JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 153 (01) :187-202
[10]   STABLE AND UNSTABLE GROWTH IN MOLECULAR-BEAM EPITAXY [J].
JOHNSON, MD ;
ORME, C ;
HUNT, AW ;
GRAFF, D ;
SUDIJONO, J ;
SANDER, LM ;
ORR, BG .
PHYSICAL REVIEW LETTERS, 1994, 72 (01) :116-119