IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v449y2016icp176-191.html
   My bibliography  Save this article

One-dimensional hyperbolic transport: Positivity and admissible boundary conditions derived from the wave formulation

Author

Listed:
  • Brasiello, Antonio
  • Crescitelli, Silvestro
  • Giona, Massimiliano

Abstract

We consider the one-dimensional Cattaneo equation for transport of scalar fields such as solute concentration and temperature in mass and heat transport problems, respectively. Although the Cattaneo equation admits a stochastic interpretation–at least in the one-dimensional case–negative concentration values can occur in boundary-value problems on a finite interval. This phenomenon stems from the probabilistic nature of this model: the stochastic interpretation provides constraints on the admissible boundary conditions, as can be deduced from the wave formulation here presented. Moreover, as here shown, energetic inequalities and the dissipative nature of the equation provide an alternative way to derive the same constraints on the boundary conditions derived by enforcing positivity. The analysis reported is also extended to transport problems in the presence of a biasing velocity field. Several general conclusions are drawn from this analysis that could be extended to the higher-dimensional case.

Suggested Citation

  • Brasiello, Antonio & Crescitelli, Silvestro & Giona, Massimiliano, 2016. "One-dimensional hyperbolic transport: Positivity and admissible boundary conditions derived from the wave formulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 176-191.
    • Handle: RePEc:eee:phsmap:v:449:y:2016:i:c:p:176-191
    DOI: 10.1016/j.physa.2015.12.111
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437115011486
    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.2015.12.111?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:449:y:2016:i:c:p:176-191. 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.