Global Attractor for a Fourth-Order Parabolic Equation Modeling Epitaxial Thin Film Growth

• Autorzy: Duan N. , Zhao X.

Identyfikatory

DOI

10.4064/ba60-3-6

• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with a fourth-order parabolic equation which models epitaxial growth of nanoscale thin films. Based on the regularity estimates for semigroups and the classical existence theorem of global attractors, we prove that the fourth order parabolic equation possesses a global attractor in a subspace of H², which attracts all the bounded sets of H² in the H²-norm.

Słowa kluczowe

EN

global attractor; fourth order parabolic equation; absorbing set

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: Vol. 60, no 3
• Strony: 259--268
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Duan N.

• College of Mathematics Jilin University Changchun, P.R. China, 130012

autor

Zhao X.

• College of Mathematics Jilin University Changchun, P.R. China, 130012

Bibliografia

• [1] J. W. Cholewa and T. Dlotko, Global attractor for the Cahn{Hilliard system, Bull. Austral. Math. Soc. 49 (1994), 277{292.
• [2] T. Dlotko, Global attractor for the Cahn{Hilliard equation in H2 and H3, J. Differential Equations 113 (1994), 381{393.
• [3] J. K. Hale, Asymptotic Behavior of Dissipative Systems, Amer. Math. Soc., Providence, RI, 1988.
• [4] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer, New York, 1981.
• [5] B. B. King, O. Stein and M. Winkler, A fourth order parabolic equation modeling epitaxial thin film growth, J. Math. Anal. Appl. 286 (2003), 459{490.
• [6] V. R. Kohn and X. Yan, Upper bound on the coarsening rate for an epitaxial growth model, Comm. Pure Appl. Math. 56 (2003), 1549{1564.
• [7] R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer, New York, 1988.
• [8] A. Zangwill, Some causes and a consequence of epitaxial roughening, J. Crystal Growth 163 (1996), 8{21.
• [9] X. P. Zhao and C. C. Liu, The existence of global attractor for a fourth-order parabolic equation, Appl. Anal., in press.
• [10] S. M. Zheng, Asymptotic behavior of solution to the Cahn{Hilliard equation, Appl. Anal. 23 (1986), 165{184.