IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i9p3042-3080.html
   My bibliography  Save this article

Coagulation, diffusion and the continuous Smoluchowski equation

Author

Listed:
  • Yaghouti, Mohammad Reza
  • Rezakhanlou, Fraydoun
  • Hammond, Alan

Abstract

The Smoluchowski equations are a system of partial differential equations modelling the diffusion and binary coagulation of a large collection of tiny particles. The mass parameter may be indexed either by positive integers or by positive reals, these corresponding to the discrete or the continuous form of the equations. For dimension d>=3, we derive the continuous Smoluchowski PDE as a kinetic limit of a microscopic model of Brownian particles liable to coalesce, using a method similar to that used to derive the discrete form of the equations in [A. Hammond, F. Rezakhanlou, The kinetic limit of a system of coagulating Brownian particles, Arch. Ration. Mech. Anal. 185 (2007) 1-67]. The principal innovation is a correlation-type bound on particle locations that permits the derivation in the continuous context while simplifying the arguments of the cited work. We also comment on the scaling satisfied by the continuous Smoluchowski PDE, and its potential implications for blow-up of solutions of the equations.

Suggested Citation

  • Yaghouti, Mohammad Reza & Rezakhanlou, Fraydoun & Hammond, Alan, 2009. "Coagulation, diffusion and the continuous Smoluchowski equation," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 3042-3080, September.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:9:p:3042-3080
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(09)00074-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Citations

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


    Cited by:

    1. Azikri de Deus, Hilbeth P. & Silva, Thales A. Barbosa Pinto & Itskov, Mikhail, 2019. "An analysis on the shear modulus of the modified Jeffreys model," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 649-665.

    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:spapps:v:119:y:2009:i:9:p:3042-3080. 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.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.