IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-94-010-1745-9_8.html
   My bibliography  Save this book chapter

Mean Values Connected with the Sawtooth Curve of Figure 5

In: The Nonlinear Diffusion Equation

Author

Listed:
  • J. M. Burgers

    (University of Maryland, Institute for Fluid Dynamics and Applied Mathematics)

Abstract

For large values of t the solution of the nonlinear Equation (1.1), with v→0, asymptotically approaches to a ‘sawtooth’ curve, consisting of upward sloping segments, having a slope equal to 1/t, separated by steep vertical descents or ‘shocks’, as indicated in Figure 5 and in more detail in the lower part of Figure 13 . The location of a ‘shock’ is determined by the position of the axis of the doubly contacting parabola at the instant t under consideration and is denoted by x k . The endpoints of the parabolic arc are at x k + x ′ k $${x_k} + {x'_k}$$ and x k + x ′ ″ k $${x_k} + {x'''_k}$$ so that x k ′ and x k ″ are relative coordinates with reference to the axis of the parabola They correspond to x 1, x 2, respectively, occurring in the integrals of the preceding chapter.

Suggested Citation

  • J. M. Burgers, 1974. "Mean Values Connected with the Sawtooth Curve of Figure 5," Springer Books, in: The Nonlinear Diffusion Equation, chapter 0, pages 124-131, Springer.
    • Handle: RePEc:spr:sprchp:978-94-010-1745-9_8
    DOI: 10.1007/978-94-010-1745-9_8
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    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:spr:sprchp:978-94-010-1745-9_8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.