Startseite On the solutions of a fourth order parabolic equation modeling epitaxial thin film growth
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On the solutions of a fourth order parabolic equation modeling epitaxial thin film growth

  • Ning Duan EMAIL logo , Xiaopeng Zhao und Xiufang Zhao
Veröffentlicht/Copyright: 23. August 2016
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 66 Heft 3

Abstract

In this paper, we study the existence and uniqueness of global weak solution, the regularity of the solutions and the existence of global attractor for a fourth order parabolic equation modeling epitaxial thin film growth with Neumann boundary conditions in two space dimensions.

MSC 2010: Primary 35B41, 35K35, 35K55; Secondary 76A20
Keywords: fourth order parabolic equation; existence; uniqueness; regularity; global attractor

(Communicated by Andras Ronto)

Acknowledgement

The authors would like to thank the editor and the anonymous referees for the valuable comments and suggestions about this paper.

References

[1] Dlotko, T.: Global attractor for the Cahn-Hilliard equation in H2 and H3, J. Differential Equations 113 (1994), 381–393.10.1006/jdeq.1994.1129Suche in Google Scholar

[2] Giaquinta, M.: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic System, Princeton Univ. Press, Princeton, NJ, 1983.10.1515/9781400881628Suche in Google Scholar

[3] Hale, J. K.: Asymptotic Behaviour of Dissipative Systems, Amer. Math. Soc., Providence, RI, 1988.Suche in Google Scholar

[4] King, B. B.—Stein, O.—Winkler, M.: A fourth-order parabolic equation modelling epitaxial thin film growth, J. Math. Anal. Appl. 286 (2003), 459–490.10.1016/S0022-247X(03)00474-8Suche in Google Scholar

[5] Kohn, V. R.—Yan, X.: Upper bound on the coarsening rate for an epitaxial growth model, Comm. Pure Appl. Math. 56 (2003), 1549–1564.10.1002/cpa.10103Suche in Google Scholar

[6] Liu, C.: Regularity of solutions for a fourth order parabolic equation, Bull. Belg. Math. Soc. Simon Stevin 13 (2006), 527–535.10.36045/bbms/1161350694Suche in Google Scholar

[7] Liu, C.: A fourth order parabolic equation with nonlinear principal part, Nonlinear Anal. 68 (2008), 393–401.10.1016/j.na.2006.11.005Suche in Google Scholar

[8] Murray, J. D.: Mathematical Biology, Springer, Berlin, 1998.Suche in Google Scholar

[9] Ortiz, M.—Repetto, E. A.—Si, H.: A continuum model of kinetic roughening and coarsening in thin films, J. Mech. Phys. Solids 47 (1999), 697–730.10.1016/S0022-5096(98)00102-1Suche in Google Scholar

[10] Temam, R.: Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1988.10.1007/978-1-4684-0313-8Suche in Google Scholar

[11] Temam, R.: Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1988.10.1007/978-1-4684-0313-8Suche in Google Scholar

[12] Yin, J.—Liu, C.: Regularity of solutions of the Cahn-Hilliard equation with concentration dependent mobility, Nonlinear Anal. 45 (2001), 543–554.10.1016/S0362-546X(99)00406-XSuche in Google Scholar

[13] Zangwill, A.: Some causes and a consequence of epitaxial roughening, J. Cryst. Growth 163 (1996), 8–21.10.1016/0022-0248(95)01048-3Suche in Google Scholar

[14] Zhao, X.—Liu, C.: The existence of global attractor for a fourth-order parabolic equation, Appl. Anal. 92 (2013), 44–59.10.1080/00036811.2011.590476Suche in Google Scholar

[15] Zhao, X.—Zhang, M.—Liu, C.: Some properties of solutions for a fourth-order parabolic equation, Math. Methods Appl. Sci. 36 (2013), 169–181.10.1002/mma.2579Suche in Google Scholar

Received: 2012-3-6
Accepted: 2013-7-22
Published Online: 2016-8-23
Published in Print: 2016-6-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0167
Schlagwörter für diesen Artikel
fourth order parabolic equation; existence; uniqueness; regularity; global attractor

Artikel in diesem Heft

  1. Research Article
  2. On the vertex-to-edge duality between the Cayley graph and the coset geometry of von Dyck groups
  3. Research Article
  4. Characterization of hereditarily reversible posets
  5. Research Article
  6. Families of sets which can be represented as sublattices of the lattice of convex subsets of a linearly ordered set
  7. Research Article
  8. Diophantine equation X4+Y4 = 2(U4 + V4)
  9. Research Article
  10. On the congruent number problem over integers of cyclic number fields
  11. Research Article
  12. On the Diophantine equation x2 + C= yn for C = 2a3b17c and C = 2a13b17c
  13. Research Article
  14. Representations and evaluations of the error term in a certain divisor problem
  15. Research Article
  16. A construction of a Peano curve
  17. Research Article
  18. Compositions of ϱ-upper continuous functions
  19. Research Article
  20. Products of Świa̧tkowski functions
  21. Research Article
  22. Subclasses of meromorphically p-valent functions involving a certain linear operator
  23. Research Article
  24. Oscillation results for second-order mixed neutral differential equations with distributed deviating arguments
  25. Research Article
  26. Oscillation criteria for higher order nonlinear delay dynamic equations on time scales
  27. Research Article
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  30. Meromorphic solutions of q-shift difference equations
  31. Research Article
  32. Oscillation criteria for higher-order nonlinear delay dynamic equations on time scales
  33. Research Article
  34. Multiplier spaces and the summing operator for series
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  36. Weighted αβ-statistical convergence of Kantorovich-Mittag-Leffler operators
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  47. Research Article
  48. Closed form evaluation of sums containing squares of Fibonomial coefficients
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