# Trimester Seminar

## Venue: HIM, Poppelsdorfer Allee 45, Lecture Hall

## Seminar Series *Coagulation-fragmentation*

*(weekly at times to be determined)*

## Thursday, July 18

14:00 |
Robert Pego (Carnegie Mellon University): Universal dynamics of heavy tails in branching processes |

15:00 |
Marina Ferreira (Helsinki): Coagulation equations with source for aerosol dynamics |

## Friday, July 12

10:00 |
Alessia Nota (Bonn): The linear Smoluchowski equation: derivation from a particle system and long time behaviour |

**Abstract**In this talk we consider the coalescence dynamics of a tagged particle in a random distribution of fixed particles with volumes independently distributed according to a suitable probability distribution. We present a rigorous derivation of a kinetic equation for the probability density for the size and position of the tagged particle in the kinetic limit where the volume fraction filled by the background of particles tends to zero. Moreover, we prove that the particle system is well posed for a small but finite volume fraction with probability one. We also show that the solutions of the kinetic equation derived yield a rich structure of asymptotic behaviours. In particular, under suitable assumptions on the distribution of volumes a self-similar behaviour of the solutions for long times might be expected.

## Thursday, July 4

15:00 |
Maxime Breden (Munich): Moments estimates for the diffusive coagulation-fragmentation equations |

16:00 |
Coffee break |

16:30 |
Bertrand Lods (Turin): Long time behaviour of a kinetic model for annihilation |

## Seminar Series: Homogenization of Reaction-Diffusion systems and related topics

**First seminar: Wednesday, 12 June between 2.30 pm to 4.00 pm**

**Second seminar: Thursday, 13 June between 2.30 pm to 4.00 pm**

**Third seminar: Friday, 14 June between 2.30 pm to 4.00 pm**

**Speaker: Harsha Hutridurga (Indian Institute of Technology Bombay)**

#### Abstract

In these seminars, we address certain periodic homogenization problems of reaction-diffusion systems arising in the context of reversible chemistry. We try to highlight the main difficulties involved in the mathematical analysis of such models. The importance of the entropy dissipation structure of the rate functions involved in reversible chemical kinetics will be emphasised. We will be working with multiplier based energy method as applicable to these systems and the parabolic duality estimates. We also hope to highlight some of the open questions related to these models. For homogenization purposes, we will be employing the method of two-scale convergence, which will be briefly introduced during the lectures.