IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v635y2024ics0378437123010300.html
   My bibliography  Save this article

A family of nonlinear diffusion equations related to the q-error function

Author

Listed:
  • Plastino, A.R.
  • Tsallis, C.
  • Wedemann, R.S.

Abstract

We investigate a bi-parametric family of nonlinear diffusion equations that includes, as special members, the power-law nonlinear diffusion equation, and an evolution equation akin to Ubriaco’s nonlinear diffusion equation. It is well-known that the power-law nonlinear diffusion equation is closely related to the Sq-thermostatistics. We show that the Ubriaco-like member of the above mentioned bi-parametric family is also related to the Sq-theory, because it admits exact time-dependent solutions that exhibit the q-error-function shape. These solutions constitute a generalization, within the Sq-thermostatistical framework, of a celebrated class of solutions of the linear diffusion equation, that have the standard error-function form. Besides exploring the main aspects of a family of non-standard diffusion processes, our present developments constitute a physical-mathematical application of the q-error-function. This function, in spite of its potential relevance for q-statistics and its applications, has not yet attracted the attention it deserves from the Sq-thermostatistics research community.

Suggested Citation

  • Plastino, A.R. & Tsallis, C. & Wedemann, R.S., 2024. "A family of nonlinear diffusion equations related to the q-error function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 635(C).
    • Handle: RePEc:eee:phsmap:v:635:y:2024:i:c:s0378437123010300
    DOI: 10.1016/j.physa.2023.129475
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437123010300
    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.2023.129475?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.

    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:635:y:2024:i:c:s0378437123010300. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.