IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v345y2005i3p457-471.html
   My bibliography  Save this article

Further transformation properties of generalised inhomogeneous nonlinear diffusion equations with variable coefficients

Author

Listed:
  • Sophocleous, Christodoulos

Abstract

We consider the variable coefficient inhomogeneous nonlinear diffusion equations of the form xput=[xqunux]x. We present further transformation properties for this nonlinear class of equations that do not appear in the literature. In particular, we map this class of variable-coefficient into constant-coefficient evolution equations. We also introduce hodograph and generalised hodograph transformation. For a specific form of this class we derive an auto-hodograph transformation. New nonlocal symmetries known as potential symmetries are found. Finally, examples of exact solutions are given.

Suggested Citation

  • Sophocleous, Christodoulos, 2005. "Further transformation properties of generalised inhomogeneous nonlinear diffusion equations with variable coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(3), pages 457-471.
    • Handle: RePEc:eee:phsmap:v:345:y:2005:i:3:p:457-471
    DOI: 10.1016/j.physa.2004.07.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437104010040
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2004.07.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sophocleous, Christodoulos, 2003. "Symmetries and form-preserving transformations of generalised inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 509-529.
    2. Sophocleous, Christodoulos, 2003. "Classification of potential symmetries of generalised inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 169-183.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Feng, Wei & Ji, Lina, 2013. "Conditional Lie–Bäcklund symmetries and functionally separable solutions of the generalized inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 618-627.
    2. Ivanova, N.M. & Popovych, R.O. & Sophocleous, C. & Vaneeva, O.O., 2009. "Conservation laws and hierarchies of potential symmetries for certain diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 343-356.
    3. Ji, Lina, 2010. "Conditional Lie–Bäcklund symmetries and solutions of inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5655-5661.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Feng, Wei & Ji, Lina, 2013. "Conditional Lie–Bäcklund symmetries and functionally separable solutions of the generalized inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 618-627.
    2. Ji, Lina, 2010. "Conditional Lie–Bäcklund symmetries and solutions of inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5655-5661.
    3. Gandarias, M.L., 2008. "New potential symmetries for some evolution equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(10), pages 2234-2242.
    4. Sophocleous, Christodoulos, 2003. "Symmetries and form-preserving transformations of generalised inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 509-529.
    5. Ivanova, N.M. & Popovych, R.O. & Sophocleous, C. & Vaneeva, O.O., 2009. "Conservation laws and hierarchies of potential symmetries for certain diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 343-356.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:345:y:2005:i:3:p:457-471. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.