05/09/2016, 16:20 — 17:00 — Amphitheatre Pa2, Mathematics Building
João Teixeira Pinto, Instituto Superior Técnico, Universidade de Lisboa

Center manifolds and rates of convergence to scaling profiles in a deposition model

We consider a coagulation type system modeling submonolayer deposition. This study focuses on establishing asymptotic scaling (or similarity) profiles and rates of convergence of the solutions to those profiles. In an earlier study (Costin et al. in Commun. Inf. Syst., 13 (3013), pp. 183-200), other authors have established those scaling profiles by using asymptotic expansions methods. However, in order to aditionally obtain the above mentioned rates of convergence, higher order estimates are needed. Here we show how center manifolds estimates provide an alternative way of establishing those profiles while obtaining, at the same time, those required higher order estimates. A new interesting feature we prove is that, although the memory of the initial condition is completely lost in the limiting profile, the rate of convergence to this profile preserve information about the large cluster tail of the initial condition.

This is a joint work with Fernando Pestana da Costa and Rafael Sasportes.