Seminar series on Coagulation and fragmentation dynamics

mardi 29 sept. 2026, 10:00 → mardi 20 oct. 2026, 17:00 Europe/Paris

A short series of seminars will run throughout the fall 2026. The seminars will run in a hybrid format, taking place at the Institut de Mathématiques de Toulouse and streamed on the links given below. Each seminar lasts 1 hour, including questions.

 

29 Sep	11:15 a.m.	Inmaculada Berral (University of Granada)	Link to the streaming	Quantitative Metastability in the Linear Becker–Döring Equations
6 Oct	11:15 a.m.	Eugenia Franco (University of Bonn)		Long-time behaviour of a two-component coagulation model for rouleau formation
20 Oct	9:50 a.m.	Marina Ferreira (University of Toulouse, CNRS)		Localization and fluctuations in non-equilibrium multicomponent coagulating systems

 

Abstracts:

Inmaculada Berral: Quantitative Metastability in the Linear Becker–Döring Equations

The Becker–Döring equations describe the dynamics of cluster formation and have long been known to exhibit metastable behaviour near the critical monomer concentration. In the linear setting, where the monomer concentration is fixed, Penrose [3, 2] and Kreer [1] established fundamental results on the metastable regime and the long-time behaviour of solutions. 
In this talk, we revisit this metastable behaviour from a quantitative perspective. We study the convergence of solutions to equilibrium in the subcritical and supercritical regimes and obtain explicit estimates for the exponential relaxation rate. Our approach combines entropy methods with discrete Hardy inequalities and relates the convergence rate to the spectral properties of the associated linear operator.
We show that, as the critical concentration is approached, the relaxation rate becomes small, providing a quantitative description of the metastable time scale. In the supercritical regime, we also identify the role of the critical cluster size and the exponentially small flux through it, which provides a natural interpretation of the slow relaxation.

 

Eugenia Franco: Long-time behaviour of a two-component coagulation model for rouleau formation

We study a two-component coagulation equation that models the aggregation of rouleaux in blood. We consider product kernels that have homogeneity 2 and we characterize the initial data that lead to gelation. We prove that, when gelation occurs, the solution to the two-component
coagulation equation localizes along a direction of the space of cluster as t approaches the gelation time 0<T∗ <∞. The localization direction is determined by the initial datum. We also prove that the solution
converges to a self-similar solution along the direction of localization.

 

Marina Ferreira: Localization and fluctuations in non-equilibrium multicomponent coagulating systems

We consider the multicomponent Smoluchowski coagulation equation under non-equilibrium conditions induced either by a source term or via a constant flux constraint. We prove that the corresponding stationary non-equilibrium solutions have a universal localization property: they asymptotically localize into a direction determined by the source or by a flux constraint. As a consequence, the ratio between monomers of a given type to the total number of monomers in the cluster becomes ever closer to a predetermined ratio as the cluster size is increased. Moreover, under an extra symmetry assumption on the coagulation kernel, the fluctuations around the localization direction of the quotient of the multicomponent solution and the one-component solution converge to a multivariate Gaussian probability density function, which is independent of the coagulation kernel.