University of Birmingham > Talks@bham > Analysis Seminar > Selfsimilar solutions to Smoluchowski's coagulation equation in singular and non singular cases

Selfsimilar solutions to Smoluchowski's coagulation equation in singular and non singular cases

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact José Cañizo.

Smoluchowski’s coagulation equation is a mean field model describing cluster growth that has been used in a very wide set of applications, ranging from physical chemistry to astrophysics and population dynamics. For a good introductory survey, see [2] and the references therein.

Many dynamical properties depend on the integration kernel $K\left(x,y\right)$, which determines the reactivity between couples of masses. It is known that, for certain kernels such as $K_{*}=xy$, a singularity in finite time occurs: the solution develops a heavy tail in finite time and the total mass is no longer conserved. This phenomenon is called gelation and represents the formation of a cluster with infinite density that drains mass from the coagulating system.

In this talk we will consider homogeneous kernels $K\left(x,y\right)=\left(xy\right)^{\lambda}$ with $\lambda \le1$ and present some results about selfsimilar solutions both in singular and non singular cases. Such self-similar solutions depend on a free exponent that cannot be determined from dimensional considerations -self-similar solution of the second kind, in the notation of Barenblatt [1]; it can be fixed imposing the behaviour at the origin and infinity. This is joint work with Marco A. Fontelos.


  1. Barenblatt, G.I., Scaling, self-similarity, and intermediate asymptotics (Cambridge texts in applied Mathe- matics: Cambridge University Press) 1996.
  2. Leyvraz, F., Scaling theory and exactly solved models in the kinetics of irreversible aggregation, Phys. Rep. 383 (2003), 95 .
  3. Smoluchowski, M., Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen, Phys Z, 17 (1916) 557—571 and 585—599.

This talk is part of the Analysis Seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


Talks@bham, University of Birmingham. Contact Us | Help and Documentation | Privacy and Publicity.
talks@bham is based on from the University of Cambridge.