Skip to main content
SpringerLink
Log in

Group Classification, Reductions and Exact Solutions of a Class of Higher Order Nonlinear Degenerate Parabolic Equation

  • Original Paper
  • Published:
International Journal of Applied and Computational Mathematics Aims and scope Submit manuscript

Abstract

A complete group classification of the nonlinear degenerate parabolic equation is presented and symmetry generators are calculated for each f(u). For arbitrary f(u), one dimensional conjugacy classes for symmetry algebras are obtained and similarity reduction of each class is given. Moreover, exact solutions for some particular cases are also presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bernis, F., Friedman, A.: Higher order nonlinear degenerate parabolic equations. J. Differ. Equ. 83, 179–206 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Fine, H.B.: Singular solutions of ordinary differential equations. Am. J. Math. 12(3), 295–322 (1890)

    Article  MathSciNet  MATH  Google Scholar 

  3. Greenspan, H.P.: On the motion of a small viscous droplet that wets a surface. J. Fluid Mech. 84, 125–143 (1978)

    Article  MATH  Google Scholar 

  4. Greenspan, H.P., Mccay, B.M.: On the wetting of a surface by a very viscous fluid. Stud. Appl. Math. 64, 95–112 (1981)

    MathSciNet  MATH  Google Scholar 

  5. Hocking, L.M.: Sliding and spreading of thin two-dimensional drops. Q. J. Mech. Appl. Math. 34, 37–55 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  6. Lacey, A.A.: The motion with slip of a thin viscous droplet over a solid surface. Stud. Appl. Math. 67, 217–230 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ren, W., Trinh, P.H., Weinan, E.: On the distinguished limits of the Navier slip model of the moving contact line problem. J. Fluid Mech. https://doi.org/10.1017/jfm.2015.173

  8. King, J.R.: The isolation oxidation of silicon. SIAM J. Appl. Math. 49(1), 264–280 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  9. Smyth, N.F., Hill, J.M.: High order nonlinear diffusion. IMA J. Appl. Math. 40, 73–86 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ivanova, N.M., Sophocleous, C.: On the group classification of variable-coefficient nonlinear diffusion convection equations. J. Comput. Appl. Math. 197(15), 322–344 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Vaneeva, O.O., Johnpillai, A.G., Popovych, R.O., Sophocleous, C.: Group analysis of nonlinear fin equations. Appl. Math. Lett. 21, 248–253 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ulusoy, S.: A new family of higher order nonlinear degenerate parabolic equations. Nonlinearity 20, 685–712 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ovsyannikov, L.V.: Group Analysis of Differential Equations. Academic Press, New York (1982)

    MATH  Google Scholar 

  14. Gandarias, M.L., Medina, E.: Analysis of a lubrication model through symmetry reductions. Europhys. Lett. 55(2), 143–149 (2001)

    Article  MATH  Google Scholar 

  15. Clarkson, P.A., Mansfield, E.L.: Symmetry reductions and exact solutions of a class of nonlinear heat equation. Phys. D 70(3), 250–288 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  16. Olver, P.J.: Applications of Lie Groups to Differential Equations. Springer, New York (1986)

    Book  MATH  Google Scholar 

  17. Patera, J., Winternitz, P.: Subalgebras of real three- and four-dimensional Lie algebras. J. Math. Phys. 18(7), 1449–1455 (1977)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Deanship of Educational Services, Preparatory Year Unit, Qassim University, P.O. Box 6595, Buraidah, Al-Qassim, 51452, Kingdom of Saudi Arabia

    Adil Jhangeer

Authors
  1. Adil Jhangeer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adil Jhangeer.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jhangeer, A. Group Classification, Reductions and Exact Solutions of a Class of Higher Order Nonlinear Degenerate Parabolic Equation. Int. J. Appl. Comput. Math 4, 2 (2018). https://doi.org/10.1007/s40819-017-0451-0

Download citation

  • Published:

  • DOI: https://doi.org/10.1007/s40819-017-0451-0

Keywords

Search

Navigation