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Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 3
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Articles

Some properties of solutions for a parabolic equation modeling epitaxial thin film growth

Pages 584-598 | Received 10 Nov 2014, Accepted 09 Feb 2015, Published online: 16 Mar 2015

References

  • King BB, Stein O, Winkle M. A fourth order parabolic equation modeling epitaxial thin film growth. J. Math. Anal. Appl. 2003;286:459–490.
  • Zhao X, Liu C. The existence of global attractor for a fourth-order parabolic equation. Appl. Anal. 2013;92:44–59.
  • Zangwill A. Some causes and a consequence of epitaxial roughening. J. Cryst. Growth. 1996;163:8–21.
  • Blowey JF. Finite element approximation of the Cahn–Hilliard equation with concentration dependent mobility. Math. Comp. 1999;68:487–517.
  • Yin J. On the Cahn–Hilliard equation with nonlinear principal part. J. Part. Differ. Equ. 1994;7:77–96.
  • Zhao X, Liu C, Liu B. Global attractor for a fourth-order parabolic equation. J. Inf. Comp. Sci. 2010;7:1819–1825.
  • Liu C. Regularity of solutions for a fourth order parabolic equation. Bull. Belg. Math. Soc. Simon Stevin. 2006;13:527–535.
  • Liu C. A fourth order parabolic equation with nonlinear principal part. Nonlinear Anal. 2008;68:393–401.
  • Fujimura H, Yagi A. Dynamical system for a BCF model describing crystal surface growth, Vestnik Chelyab. Univ. Ser. 3 Mat. Mekh. Inform. 2008;10:75–88.
  • Fujimura H, Yagi A. Asymptotic behavior of solutions for BCF model describing crystal surface growth. Int. Math. Forum. 2008;3:1803–1812.
  • Fujimura H, Yagi A. Homogeneous stationary solution for BCF model describing crystal surface growth. Sci. Math. Jpn. 2009;69:295–302.
  • Grasselli M, Mola G, Yagi A. On the longtime behavior of solutions to a model for epitaxial growth. Osaka J. Math. 2011;48:987–1004.
  • Zhao X, Liu C. Global attractor for a nonlinear model with periodic boundary value condition. Portugaliae Mathematica. 2012;69:221–231.
  • Duan N, Zhao X. Global attractor for a fourth-order parabolic equation modeling epitaxial thin film growth. Bull. Pol. Acad. Sci. Math. 2012;60:259–268.
  • Liu C, Li Z. Existence of solutions for a nonlocal epitaxial thin film growing equation. Arch. Math. 2012;99:157–168.
  • Temam R. Infinite-dimensional dynamical systems in mechanics and physics. New York (NY): Springer-Verlag; 1988.
  • Song L, Zhang Y, Ma T. Global attractor of the Cahn-Hilliard equation in Hk space. J. Math. Anal. Appl. 2009;355:53–62.
  • Song L, He Y, Zhang Y. The existence of global attractors for semilinear parabolic equation in Hk space. Nonlinear Anal. 2008;68:3541–3549.
  • Song L, Zhang Y, Ma T. Global attractor of a modified Swift-Hohenberg equation in Hk space. Nonlinear Anal. 2010;72:183–191.
  • Ma T, Wang S. Stability and bifurcation of nonlinear evolution equations. Beijing: Science Press; 2006. Chinese.

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