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Mathematica Slovaca

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A sixth order degenerate equation with the higher order p-laplacian operator

Changchun Liu
  • Jilin University
  • :
Published Online: 2010-12-12 | DOI: https://doi.org/10.2478/s12175-010-0052-4

Abstract

We consider a initial-boundary value problem for a sixth order degenerate parabolic equation. Under some assumptions on the initial value, we establish the existence of weak solutions by the time-discrete method. The uniqueness, asymptotic behavior and the finite speed of propagation of perturbations of solutions are also discussed.

MSC: Primary 35D05, 35B40, 35G30, 35K55

Keywords: sixth order parabolic equation k[existence; asymptotic behavior

  • [1] ANSINI, L. —GIACOMELLI, L.: Doubly nonlinear thin film equations in one space dimension, Arch. Ration. Mech. Anal. 173 (2004), 89–131. http://dx.doi.org/10.1007/s00205-004-0313-x [Crossref]

  • [2] BERNIS, F.: Qualitative properties for some nonlinear higher order degenerate parabolic equations, Houston J. Math. 14 (1988), 319–352.

  • [3] CHANG, K.: Critical Point Theory and Its Applications, Shanghai Sci. Tech. Press, Shanghai, 1986.

  • [4] CHEN, Y. WU, L.: Second Order Elliptic Equations and Elliptic Systems, Science Press, Beijing, 1991.

  • [5] EVANS, J. D. —GALAKTIONOV, V. A. —KING, J. R.: Unstable sixth-order thin film equation. I. Blow-up similarity solutions, Nonlinearity 20 (2007), 1799–1841. http://dx.doi.org/10.1088/0951-7715/20/8/002 [Crossref] [Web of Science]

  • [6] FLITTON, J. C. —KING, J. R.: Moving-boundary and fixed-domain problems for a sixthorder thin-film equation, European J. Appl. Math. 15 (2004), 713–754. http://dx.doi.org/10.1017/S0956792504005753 [Crossref]

  • [7] HARDY, G. H. —LITTLEWOOD, J. E. —P’OLYA, G.: Inequalities, Cambridge University press, Cambridge, 1952.

  • [8] KING, J. R.: Two generalisations of the thin film equation, Math. Comput. Modelling 34 (2001), 737–756. http://dx.doi.org/10.1016/S0895-7177(01)00095-4 [Crossref]

  • [9] LIU, C. —YIN, J. —GAO, H.: A generalized thin film equation, Chinese Ann. Math. Ser. B 25 (2004), 347–358. http://dx.doi.org/10.1142/S0252959904000329 [Crossref]

  • [10] SIMON, J.: Compact sets in the space L p(0, T;B), Ann. Math. Pure Appl. 146 (1987), 65–96. http://dx.doi.org/10.1007/BF01762360

  • [11] XU, M. ZHOU, S.: Existence and uniqueness of weak solutions for a generalized thin film equation, Nonlinear Anal. 60 (2005), 755–774. http://dx.doi.org/10.1016/j.na.2004.01.013 [Crossref]


Published Online: 2010-12-12

Published in Print: 2010-12-01


Citation Information: Mathematica Slovaca. Volume 60, Issue 6, Pages 847–864, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-010-0052-4, December 2010

© 2010 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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